The centripetal acceleration of the Ferris wheel with radius of 14.0 m is determined as 2.57 m/s².
What is centripetal acceleration?Centripetal acceleration, is the acceleration of a body moving a circular path.
The centripetal acceleration of the Ferris wheel is calculated as follows;
a = v²/r
where;
v is the linear speedr is the radius of the circular patha = (6²) / (14)
a = 2.57 m/s²
Thus, the centripetal acceleration of the Ferris wheel is determined as 2.57 m/s².
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The complete question is below:
A Ferris wheel has a radius of 14 m, the linear speed of a passenger on the rim is 6 m/s .Find the centripetal acceleration of the Ferris wheel.
A pelican flying along a horizontal path drops a fish from a height of 7.8 m. The fish travels 12.0 m horizontally before it hits the water below. What is the pelican’s initial speed? At what velocity does the fish hit the water?
Answer:
The pelican was travelling at approximately [tex]9.5\; {\rm m\cdot s^{-1}}[/tex] when it dropped the fish.
The fish hit the water at approximately [tex]16\; {\rm m\cdot s^{-1}}[/tex].
(Assumption: air resistance on the fish is negligible; [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].)
Explanation:
During the descent:
In the horizontal direction, the fish travels at a constant velocity.In the vertical direction, the fish accelerates downwards at a constant rate of [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] under gravity.Since acceleration in the vertical direction is constant, make use of the SUVAT equation [tex]x = (1/2)\, a\, t^{2} + v_{0}\, t[/tex] to find the duration [tex]t[/tex] of the descent:
The vertical position of the fish changed by [tex]x = 7.8\; {\rm m}[/tex] during the entire descent. The vertical acceleration of the fish is [tex]a = g = 9.81\; {\rm m\cdot s^{-2}}[/tex]The pelican was flying horizontally when it dropped the fish. Thus, the initial velocity of the fish in the vertical direction is [tex]v_{0} = 0\; {\rm m\cdot s^{-1}}[/tex]. The equation becomes [tex]x = (1/2)\, a\, t^{2}[/tex].Rearrange this equation to find the duration of the descent, [tex]t[/tex]:
[tex]\begin{aligned} t &= \sqrt{\frac{2\, x}{a}} \\ &= \sqrt{\frac{2 \times 7.8\; {\rm m}}{9.81 \; {\rm m\cdot s^{-2}}} \\ &\approx 1.261\; {\rm s}\end{aligned}[/tex].
The vertical speed of the fish right before impact would be:
[tex]\begin{aligned} v_{y} &= a\, t \\ &\approx 9.81\; {\rm m\cdot s^{-2}} \times 1.261\; {\rm s} \\ &\approx 12.37\; {\rm m\cdot s^{-1}} \end{aligned}[/tex].
In the horizontal direction, the speed of the fish was constant- same as the initial speed of the pelican. The fish travelled a horizontal distance of [tex]x = 12.0 \; {\rm m}[/tex] within the [tex]t \approx 1.26\; {\rm s}[/tex] of the descent. As a result, the horizontal velocity of the fish would be:
[tex]\begin{aligned} v_{x} &= \frac{x}{t}\\ &\approx \frac{12.0\; {\rm m}}{1.261\; {\rm s}} \\ &\approx 9.52\; {\rm m\cdot s^{-1}} \end{aligned}[/tex].
Hence, the initial speed of the pelican would be approximately [tex]9.5\; {\rm m\cdot s^{-1}}[/tex].
Thus, right before impact:
The fish would be travelling at a horizontal velocity of [tex]v_{x} \approx 9.52\; {\rm m\cdot s^{-1}}[/tex].The fish would be travelling at a vertical velocity of [tex]v_{y} \approx 12.37\; {\rm m \cdot s^{-1}}[/tex].Apply the Pythagorean Theorem to find the overall velocity of the fish at that moment:
[tex]\begin{aligned} v &= \sqrt{{v_{x}}^{2} + {v_{y}}^{2}} \\ &\approx \sqrt{{(9.52\; {\rm m\cdot s^{-1}})}^{2} + {(12.37\; {\rm m\cdot s^{-1}})}^{2}} \\ &\approx 16\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
In other words, the fish would hit the water at approximately [tex]16\; {\rm m\cdot s^{-1}}[/tex].
the velocity (v) of dimension of a, b and c.
According to the given statement The dimension of a, b and c is LT⁻² , L and T.
What do we mean by dimension?She took exact measurements of the room's length, width, height, and depth in one direction (for example, the distance between the ceiling and the floor of a room). The space was unexpectedly small in all three of its dimensions. Dimensions include length, breadth, and height. One dimension is that of a line, two dimensions are those of a square, and three dimensions are those of a cube (3D).
Briefing:According to the principle of dimensional homogenity
Dimension of v = dimension of at = dimension of b/t+c
Dimension of a = [tex]\frac{[\mathrm{v}]}{[\mathrm{t}]}=\frac{\mathrm{LT}^{-2}}{\mathrm{~T}}=\left[\mathrm{LT}^{-2}\right][/tex]
Dimension of b = [v][t]=[LT −1 T]=[L]
Dimension of c = [t]=[T]
According to the given statement The dimension of a, b and c is LT⁻² , L and T.
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Mrs. J . weighs 557 N. what is her mass?
Answer:
The mass of the person is 56.83 kg
Explanation:
W= 557 N
We know that acceleration due to gravity (g)= 9.8 m/s^2
Now,
W= mass * acceleration due to gravity
557=m * 9.8
m= 557/9.8
m= 56.83
Answer:
her mass is 55.7 Kg.
Explanation:
Weight = Mass × Acceleration
N =ma [a= g for gravitational force acting down word]
N=Mg
find M so make mass become the subject therefore,
Mass = force / gravitational acceleration [let g=10m/s^2]
m=557 / 10
m= 55.7 kg
What is the acceleration of a ball rolling 12 m/s to a stop in 3 seconds?
0.25 m/s^2
4 m/s^2
-0.25 m/s^2
-4 m/s^2
A person standing at the edge of a seaside cliff kicks a stone over the edge with a speed of vi = 15 m/s. The cliff is h = 44 m above the water's surface, as shown below.
(a) How long does it take for the stone to fall to the water?
s
(b) With what speed does it strike the water?
m/s
(a) Time taken by the stone to fall into the water will be t = 2.99 sec
(b) The speed with which the stone strikes the water will be v=32.91 m/s
(a)
As the stone is kicked horizontally so that the initial velocity of the stone will be [tex]v_{0} = 0[/tex]
For finding the time taken by the stone to fall into the water will be found using the following equation
[tex]y=v_{0}t + \frac{1}{2}at^{2}[/tex]
[tex]y= \frac{1}{2}at^{2}[/tex]
[tex]t=\sqrt{\frac{2y}{a} }[/tex]
[tex]t=\sqrt{\frac{2*(-44 m)}{(-9.8 m/m^{2} )} }[/tex]
[tex]t=2.99 s[/tex]
Time taken by the stone to fall into the water will be t = 2.99 sec
(b)
Since the ball was thrown horizontally, its velocity in the horizontal axis is constant and equal to its beginning velocity.
[tex]v_{0x} = v_{0} = 15 m/s[/tex]
Final velocity at vertical axis is
[tex]v_{y} = v_{0y} + at[/tex]
[tex]v_{y} = at[/tex]
therefore,
time = 2.99 sec
[tex]v_{y} = (-9.8 m/s^{2})(2.99 sec)\\ v_{y} = -29.3 m/s^{}[/tex]
The final velocity is,
[tex]v_{}=\sqrt{v_{0x} ^{2} + v_{y} ^{2} }[/tex]
[tex]v_{}=\sqrt{(15 m/s) ^{2} + (-29.3 m/s) ^{2} }[/tex]
v=32.91 m/s
The speed with which the stone strikes the water will be v=32.91 m/s
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You are on top of a building that is 75.0 m tall. You toss a ball straight up with an initial velocity of 33.8m / s How high does the ball travel? It goes up and then falls down to the ground below. How much time is it in the air?
1 The ball travel 58.29 m high
2. The time the ball spend in the air is 8.67 s
1. How to determine the maximum heightThe maximum height reached by the ball can be obtained as follow:
Initial velocity (u) = 33.8 m/sFinal velocity (v) = 0 m/s (at maximum height) Acceleration due to gravity (g) = 9.8 m/s²Maximum height (h) =?v² = u² – 2gh (since the ball is going against gravity)
0² = 33.8² – (2 × 9.8 × h)
0 = 1142.44 – 19.6h
Collect like terms
0 – 1142.44 = –19.6h
–1142.44 = –19.6h
Divide both side by –19.6
h = –1142.44 / –19.6
h = 58.29 m
2. How to determine the time spend by the ball in the airWe'll begin by calculating the time to reach the maximum height . This can be obtained as follow:
Initial velocity (u) = 33.8 m/sFinal velocity (v) = 0 m/s (at maximum height) Acceleration due to gravity (g) = 9.8 m/s²Time to reach maximum height (t₁) =?v = u – gt (since the ball is going against gravity)
0 = 33.8 – (9.8 × t₁)
0 = 33.8 – 9.8t₁
Collect like terms
0 – 33.8 = –9.8t₁
–33.8 = –9.8t
Divide both side by –9.8
t₁ = –33.8 / –9.8
t₁ = 3.45 s
Next, we shall determine the time take to fall to the ground
Acceleration due to gravity (g) = 9.8 m/s²Maximum height from building = 58.29 mHeight of building = 75 mTotal height (h) = 58.29 + 75 = 133.29 mTime to fall to the ground (t₂) =?h = ½gt²
133.29 = ½ × 9.8 × t₂²
133.29 = 4.9 × t₂²
Divide both side by 4.9
t₂² = 133.29 / 4.9
Take the square root of both side
t₂ = √(133.29 / 4.9)
t₂ = 5.22 s
Finally, we shall determine the time spend by the ball in the air. This is shown below:
Time to reach maximum height (t₁) = 3.45 sTime to fall to the ground (t₂) = 5.22 sTotal time (T) = ?T = t₁ + t₂
T = 3.45 + 5.22
T = 8.67 s
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how much would i weigh on the star methuselah i weigh 100 pounds
Your weigh on the star methuselah is 38 pounds.
For example, if you weigh 100 pounds on Earth, you would weigh only 38 pounds on Mercury. That's because Mercury weighs less than Earth, and therefore its gravity would pull less on your body.
The element mercury has the atomic number 80 and the symbol Hg. Formerly called hydrargyrum from the Greek words Hydor (water) and Argyros, it's also known as quicksilver (silver). the sole other metallic element that is known to be liquid at standard circumstances for temperature and pressure is the halogen bromine, while metals like cesium, gallium, and rubidium melt just above temperature. Mercury may be a heavy, silvery d-block element.
Worldwide deposits of mercury, primarily as cinnabar, are found (mercuric sulfide). Grinding either synthetic mercuric sulfide or natural cinnabar yields the red color vermilion.
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Suppose the displacement of an object is related to time according to the expression x = Bt2. What are the dimensions of B?
The supplied statement states that B has the dimensions L/T².
What does the "dimension" mean?Measurements like length, width, or height are referred to as dimensions. When you discuss an object or location's dimensions, you're referring to its size and proportions.
What are some examples of dimensions?Dimensions include length, breadth, and height. One dimension is that of a line, two dimensions are those of a square, and three dimensions are those of a cube (3D).
Briefing:Just rearranging the equation will get the dimensions.
x = Bt² ----> B= x/t²
Now you are told that x is displacement (L) and t is time (T) so sub these in.
B= L/T² Therefore the dimensions are L/T².
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Can a measurement ever be exact? Why or why not?
There is no such things as an exact measurement there can never be a perfect instrument or measurer.
What is measurement?The term measurement has to do with the process of obtaining the value of a quantity. We know that measurements are done in order to give us an idea of the magnitude of a quantity. In every measurement, there is an instrument that is used for the measurement. For instance, if I want to measure length, I may have to use a meter rule to do it.
Now, there are two ways that error could be introduced into a measurement;
1) By the instrument that is used
2) By the error of the measurer
Hence, there is no such things as an exact measurement there can never be a perfect instrument or measurer.
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1. The development of what anatomical structure is one current idea for how the Cambrian Explosion began (the so-called Evolutionary Big Bang)? The
Answer:
One idea is how, on an astronomical level, the planets can be observed to spread apart continuously.
Explanation:
Throughout various studies, many have observed that the planets continuously grow distant from each other. In fact, it is observed through our technological advances that the very galaxies are slowly drifting apart. Thus, indicating there must have been some big bang to set these galaxies and planets in motion.
Polly Protractor drives 15 kilometers North to go shopping at one mall, then drives
20 kilometers East to go shopping at another mall.
The resultant displacement of the Polly protractor is 25 km.
What is displacement?The displacement of an object is the change in the position of the object.
The displacement of the Polly protractor is calculated as follows;
d² = 15² + 20²
d = √(15² + 20²)
d = 25 km
Thus, the resultant displacement of the Polly protractor is 25 km.
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The complete question is below:
Find the resultant displacement of the Polly protractor.
Match each colored row or group on the table to the family of elements it
represents.
red depicts alkali metals, green depicts alkaline earth metals, blue depicts transition metals, and purple depicts inner transition metals.
alkali metal, any of the six chemical elements that make up Group 1 (Ia) of the periodic table—namely, lithium (Li), sodium (Na), potassium (K), rubidium (Rb), cesium (Cs), and francium (Fr).
Group 2A of the periodic table are the alkaline earth metals: beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra). They are harder and less reactive than the alkali metals of Group 1A.
transition metal, any of various chemical elements that have valence electrons—i.e., electrons that can participate in the formation of chemical bonds—in two shells instead of only one.
The period 6 inner transition metals (lanthanides) and period 7 are actinides.
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A Measuring Cylinder liquid contains a volume of 120m³ the liquid was then poured into an empty beaker of mass 51g. The total mass was then found to be 145g .Calculate the mass of the liquid
The mass of liquid in the container is 94 grams and the density of the liquid is 0.78 grams/cm³ or 780 Kg/m³.
Given in the question
The volume of the liquid = Volume of the container
= 120 cm³
Total Mass = 145 grams
Mass of the empty Beaker = 51 grams
To find
Mass of the liquid
The density of the liquid
Now,
Total Mass = Mass of LIquid + Mass of the empty Beaker
Mass of LIquid = Total Mass - Mass of the empty Beaker
Put in the value, we get
Mass of liquid = 145 - 51 grams
Mass of liquid = 94 grams
Now, Density is the ratio of the mass of the substance and the volume, the substance occupies in the space. It is not a constant value and is variable with the variation in the temperature of the substance. Its S.I. unit is Kg/m³. B ut its other commonly used unit is gram/cm³.
The density of liquid = Mass of the liquid/ Volume of the liquid
Put in the value, we get
The density of the liquid = 94/120 grams/cm³
The density of the liquid = 0.78 grams/cm³ = 780 Kg/m³
Therefore, the mass of liquid in the container is 94 grams and the density of the liquid is 0.78 grams/cm³ or 780 Kg/m³.
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Your question was incomplete. Please find the full content below.
A Measuring Cylinder liquid contains a volume of 120cm³ the liquid was then poured into an empty beaker of mass 51g. The total mass was then found to be 145g . Calculate the mass of the liquid and the density of the liquid.
What do simple machines accomplish?
A. Simple machines keep the total amount of work the same, but make work more difficult.
B. Simple machines reduce the total amount of work.
C. Simple machines increase the total amount of work.
D. Simple machines keep the total amount of work the same, but make work easier.
Answer:
D
Explanation:
"Simple machines cannot change the amount of work done, but they can reduce the effort force that is required to do the work!"
source: https://www.smore.com/u609q-simple-machines
Please Help me to solve this problem!!!!!!
Answer:
Im pretty sure its B
Explanation:
correct me if wrong
A car odometer works by counting the number of revolutions in the tires. The car tires have a 13-inch radius. It goes 675,135 tire revolutions in a month. The distance traveled in that month is ___ miles.
The distance travelled in that month is 870.92 miles
How to determine the circumferene of the tyreWe'll begin by calculating the circumference of the tyre. This can be obatined as follow:
Radius (r) = 13 inPi (π) = 3.14Circumference (C) =?C = 2πr
C = 2 × 3.14 × 13
C = 81.64 in
How to convert 81.64 inches to mile63360 inches = 1 mile
Therefore,
81.64 inches = (81.64 inches × 1 mile) / 63360 inches
81.64 inches = 0.00129 mile
How to determine the distance travelledCircumference of tyre (C) = 0.00129 mileNumber of revolution (n) = 675135 tire revolutionsDistance (d) = ?Distance = number × circumference
Distance = 0.00129 × 675135
Distance = 870.92 miles
Thus, the distance travelled in that month is 870.92 miles
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What are the three functions of the integumentary system?
According to the research, the correct option are protection, thermoregulation and immune surveillance. The three functions of the integumentary system are protection, thermoregulation, and immune surveillance.
What is the integumentary system?It is made up of a deep layer of connective tissue that is directly related to the environment in which it has the peculiarity of the abundance of collagen fibers.
In this sense, its functions include protection against mechanical, thermal, and chemical-toxic injuries and against microorganisms, regulation of body temperature, and immune surveillance and response to external agents.
Therefore, we can conclude that according to the research, the correct option are protection, thermoregulation and immune surveillance. The three functions of the integumentary system are protection, thermoregulation, and immune surveillance.
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Two small objects A and B are fixed in place and separated by a distance of 3.00 cm in a vacuum. Object A has a
charge of +2.00 С and object B has a charge of -2.00 C. How many electrons must be removed from object A and
placed on object B to make the electrostatic force into an attractive force with a magnitude of 68.0 N.
The number of electrons that must be removed from object A and placed on object B is 1.24 * [tex]10^{19}[/tex]
We know that,
E = k [tex]q_{1}[/tex] [tex]q_{2}[/tex] / r²
where,
E = Electrostatic force
k = Coulomb's constant
[tex]q_{1}[/tex], [tex]q_{2}[/tex] = Point charges
r = Distance between two charges
Given that,
[tex]q_{1}[/tex] = 2 + ne C
[tex]q_{2}[/tex] = - 2 - ne C
r = 3 cm
k = 9 * [tex]10^{9}[/tex] N m² / C²
E = - 68 N ( Since it is attractive )
- 68 = 9 * [tex]10^{9}[/tex] ( 2 - ne ) ( - 2 + ne ) / ( 3 * [tex]10^{-2}[/tex] )²
68 * [tex]10^{-4}[/tex] / 3 * [tex]10^{9}[/tex] = ( 2 - ne )²
2.27 * [tex]10^{-12}[/tex] = ( 2 - ne )²
1.5 * [tex]10^{-6}[/tex] = 2 - ne
ne = 1.98
n = 1.98 / 1.6 * [tex]10^{-19}[/tex] = 1.24 * [tex]10^{19}[/tex]
The given problem is an electrostatic attractive force because the two point charges are unlike charges. If the charges are like, then the electrostatic force will be repulsive.
Therefore, the number of electrons that must be removed from object A and placed on object B is 1.24 * [tex]10^{19}[/tex]
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A string of length 30cm has one end attached to a fixed point and the other to a mass of 100g which revolves in a horizontal circle 80 times per minute. Calculate (i) the angle of inclination of the string to the vertical, and (ii) the tension T in the string.
(i) The angle of inclination of the string to the vertical is 65⁰.
(ii) The tension in the string is determined as 2.11 N.
Angular speed of the string
The angular speed of the string is calculated as follows;
ω = 2πN/60
ω = 2π x 80/60
ω = 8.38 rad/s
Linear speed of the stringv = ωr
v = 8.38 x 0.3 m
v = 2.514 m/s
Angle of inclination of the string to the verticaltanθ = v²/rg
tan θ = (2.514²) / (0.3 x 9.8)
tan θ = 2.15
θ = arc tan(2.15)
θ = 65⁰
Tension in the stringT = mv²/r
T = (0.1 x 2.514²) / (0.3)
T = 2.11 N
Thus, the tension in the string is determined as 2.11 N.
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whats the displacement in meters of a car that travels due west at 50m/hr west between 12:00 and 4:00pm
Answer:
200m west
Explanation:
Displacement = v.t where v is the velocity of the object ad t = time
At 50m/hr for 4 hours
Displacement = 50 x 4 = 200m west of origin
A bicycle was traveling at 7.6 m/s when it decided to accelerate at a rate of 4.2 m/s² over 89 m. What was its final velocity?
The final velocity of the bicycle with initial velocity 7.6m/s and acceleration 4.2 m/s² is 28.4 m/s.
What is Velocity?
velocity is defined as the displacement per unit time.
What is Acceleration?
Acceleration is defined as the rate of change of velocity per unit time
i.e.
acceleration = (final velocity (v)-initial velocity)/time taken (t)
given:
initial velocity of the bicycle (u) = 7.6m/s
acceleration of the bicycle (a)=4.2m/s²
displacement of the bicycle=89m
using newtons third law of motion :
v²-u²=2×a×s
using the given value in question we get
v² = (7.6)²+2×4.2×89
v=28.4 m/s
the final velocity of the bicycle with initial velocity 7.6m/s and acceleration 4.2 m/s² is 28.4 m/s.
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A ball is thrown vertically upward with an initial speed of 20 m/s. Two seconds later, a stone is thrown vertically (from the same initial height as the ball) with an initial speed of 24 m/s. At what height above the release point will the ball and stone pass each other?
The correct answer is 17.12 meters.
S = VoT - (1/2)g[tex]T^2[/tex]
where
S = distance travelled by the body
Vo = initial velocity
T = travel time
g = acceleration due to gravity = 9.8 m/sec^2 (constant)
For the ball,
Sb = 20T - (1/2)(9.8)( )
and for the stone,
Ss = 24(T - 2) + (1/2)(9.8)(T - 2[tex])^2[/tex]
and for them to pass each other from the release point,
Sb = Ss
and therefore
20T - (1/2)(9.8)[tex]T^2[/tex] = 24(T - 2) - (1/2)(9.8)(T - 2[tex])^2[/tex]
20T - 4.9[tex]T^2[/tex] = 24T - 48 - 4.9([tex]T^2[/tex] - 4T + 4)
20T - 4.9[tex]T^2[/tex] = 24T - 48 - 4.9[tex]T^2[/tex] + 19.6T - 19.6
Combining like terms,
24T + 19.6T - 20T = 48 +19.6
23.6T = 67.6
T = 2.86 sec.
In other words, the stone will pass the ball 2.86 seconds after the ball has been tossed (or 0.86 sec after the stone has been tossed).
Solving for Sb,
Sb = 20(2.86) - (1/2)(9.8)([tex]2.86^2[/tex])
Sb = 17.12 meters -the ball will be passed by the stone at this elevation above the release point. This is the first option in your given choices.
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State Newton's First law of motion.
Knowing that Newton's first law is the law of inertia.
The law of inertia helps us when we have problems with bodies that are motionless or moving at constant speed.
The first law tells us that: "A body remains at rest or moves with constant speed if a resultant force equal to zero acts on it."
If the body is at rest or moves with constant speed without acceleration, then the sum of the forces in both the x, y or z axis is equal to zero.
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The total displacement of the object was 7.5 meters.
Explanation:There's a relation between the common movement analysis graphs that we can always use. These relations are the following:
The derivative (slope) of a displacement vs. time graph gives you the function of speed vs. time. Also, when you take the speed vs. time graph and find its derivative, you will get the acceleration function of the observed body.
Now, doing to opposite of derivation (integration), we are able to calculate the displacement of an object when we integrate the function of velocity vs. time. This is not a complicated process when we have a linear function, because integration is just calculating the area under the curve or line of a graph.
In this case, the graph forms a right triangle with the x axis, therefore, we are able to calculate displacement by finding the area under the line of the graph. It could also be made with integration, we are going to do it with both processes as they are both used, and in some cases you have to strictly use one of the 2 in order to get the most precise answers.
Method 1. By finding the area through geometry.When we observe the line, we can crearly tell that the area under the graph constitutes a right triangle. Hence, the area under the graph is given by the following formula:
[tex]A=\frac{bh}{2}[/tex]
Substitute the values and calculate.
(Check attached image 1 to see where the values of b and h are taken from).
[tex]A=\frac{(5)(3)}{2}\\ \\A=7.5[/tex]
Hence, the total displacement of the object was 7.5 meters.
Method 2. By integration.In this method, we'll need to find the equation of the line and then generate and solve a definite integral.
Take 2 points from the line.
(0, 0) and (5, 3).
Find the slope.
Formula: [tex]m=\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
[tex]m=\frac{3-0}{5-0}= \\ \\m= \frac{3}{5}[/tex]
Find the equation of the line.
Formula: [tex]y-y_{1} =m(x-x_{1} )[/tex]
[tex]y-(0) =\frac{3}{5} (x-(0) )\\ \\y=\frac{3}{5} x\\ \\[/tex]
Integrate within the interval of interest (from 0 to 5).
[tex]\int\limits^5_0 {(\frac{3}{5} x)} \, dx \\ \\=\frac{3}{5} x^{2} *\frac{1}{2} \\ \\=\frac{3}{10} x^{2} \\\\ (\frac{3}{10} (5)^{2})-(\frac{3}{10} (0)^{2})\\ \\(\frac{3}{10} *25)-(0)\\ \\\frac{75}{10} \\ \\7.5[/tex]
Once again, the total displacement of the object was 7.5 meters.
what is the relationship between a boats volume and the amount of mass it can hold before sinking
Answer:
Explanation:
the rilation shhip betveen boats annd volummes are ver expennsive
The buoyancy of a boat and the density of the materials used in its construction have an impact on the connection between its volume and the amount of mass it can support before sinking.
Thus, The buoyancy principle asserts that the upward force a fluid (in this case, water) exerts on a submerged or floating item is equal to the weight of the fluid displaced by the object, which is why a boat floats in water.
A boat moves as much water as its own volume while it is submerged in water.
A boat will float if its total weight, including its passengers and cargo, is less than the weight of the water it moves.
Thus, The buoyancy of a boat and the density of the materials used in its construction have an impact on the connection between its volume and the amount of mass it can support before sinking.
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What is the acceleration of a car that goes from 0 m/s to 20 m/s in 100 m?
Answer:
[tex]{ \tt{ {v}^{2} = {u}^{2} + 2as}} \\ { \tt{20 = 0 + (2 \times a \times 100)}} \\ { \tt{20 = 200a}} \\ { \tt{a = 0.1 \: {ms}^{ - 2} }}[/tex]
The graph provided represents voltage and current data for resistor R. What is the resistance of R?
Question 15 options:
4.5 Ω
0.50 Ω
2.0 Ω
9.0 Ω
Since the graph provided represents voltage and current data for resistor R, the resistance of R is 2.0 Ω
What is resistance?The resistance of a metallic material is its opposition to the flow of electric current.
Resistance is given by R = V/I where
V = voltage across resistor and I = currentWhat is the resistance of R?To find the resistance of R, we take the gradient of the graph since reistance R = V/I.
So, the resistance R = ΔV/ΔI where
ΔV = change in voltage and ΔI = change in currentR = ΔV/ΔI
= (V' - V)/(I' - I)
Taking points from the graph
(I,V) = (0, 0) and (I',V') = (4.5, 9.0)So, substituting the values of the variables into the equation, we have
R = (V' - V)/(I' - I)
= (9.0 V - 0 V)/(4.5 A - 0 A)
= 9.0 V/4.5 A
= 2.0 Ω
So, the resistance of R is 2.0 Ω
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8) A projectile of mass 0.25 kg moving at 24.0 m/s collides with and sticks to a 1.75-kg block that is connected to a spring for which k = 40.0 N/m, as in the figure below. The block is initially on a frictionless part of a horizontal surface but starts to slide on a rough section immediately after the collision. If the maximum compression of the spring is 0.5 m, what is the force of friction on the block
Answer:
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Explanation:
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A cylinder with a torque of 75.0 N
m rotates with an
angular acceleration of 8.5 rad s².
Calculate the
moment of inertia of the cylinder.
The Moment of inertia of the cylinder is equal to 8.82 Kgm².
The propensity of a force to produce or modify the rotational motion of a body is known as torque, also known as moment, or moment of force. It is a force that causes an object to twist or turn. Force and distance are multiplied to calculate torque. It has both a direction and a magnitude because it is a vector quantity. Newton-meters, or N*m, is the torque unit in the SI system.
A spinning object's change in angular velocity per unit of time is expressed quantitatively as angular acceleration, also known as rotational acceleration. It has a vector form.
Given in the question
Torque = 75 Nm
Angular acceleration = 8.5 rad/s²
Torque = Angular acceleration × moment of inertia
Put in the value, we get
Moment of inertia = 75/ 8.5
Moment of inertia = 8.82 Kgm²
So the Moment of inertia of the cylinder is equal to 8.82 Kgm².
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A child traveling 5 m/s on a sled passes her younger brother. If her average acceleration on the sledding hill is 2 m/s^2. how fast is she passes her older brother 4 s later?
Answer:
13 m/s
Explanation:
Given average acceleration a and initial velocity v0 we can compute the final velocity using the equation
a = (v - v0)/t where t is the time taken to reach final velocity from initial velocity
Here a = 2 m/s² and v0 is the initial velocity when she passes her younger brother v0 = 5m/s.
It takes t = 4 s to pass her older brother at which time her speed is v, say
Then
a = (v - v0)/t
Plugging in known values,
2 = (v - 5)/4
Switch sides:
(v- 5)/4 = 2
Multiply both sides by 4:
v - 5 = 8
v =5 + 8 = 13 m/s - the speed at which she passes her older brother