A football player runs from his own goal line to the opposing team's goal line, returning to his twenty-yard line, all in 27.0 s. Calculate his average speed and the magnitude of his average velocity. (Enter your answers in yards/s.)HINTApply the definitions of average speed and average velocity.Click the hint button again to remove this hint.(a) Calculate his average speed. ____yards/s(b) Calculate the magnitude of his average velocity. ____yards/s

a) 1 foot = 12 inches

159 feet = 159 x 12 = 1908

The distance in inches is 1908 inches

b) 1 inch = 2.54 cm

1908 inches = 1908 x 2.54 = 4846.32

The distance in centimeters is 4846.32 cm

c) 100 cm = 1 m

4846.32 cm = 4846.32/100 = 48.4632

The distance in meters is 48.4632 m

d) 1000m = 1 km

48.4632 m = 48.4632/1000 = 0.0484632

The distance in kilometers is 0.0484632 km

Add 6 and 5, then multiply by 4 is the same as 4(6 + 5). TRUE

4 times greater than 80 + 25 is the same as 4 x (80 + 25). TRUE

Subtract 15 from 42 is the same as 15 − 42. TRUE

9 times greater than 11 + 12 is the same as 9 + 11 + 12. FALSE

9 (11+12)

8 times greater than 21 + 15 is the same as 8(21 + 15). TRUE

ANSWER

EXPLANATION

To find the index of refraction of the liquid, we have to apply the formula for critical angle:

where nr = refractive index of air = 1

ni = refractive index of liquid

Hence, by substituting the given values into the equation, we have that the index of refraction of the liquid is:

That is the answer.

Given data:

* The speed of the bus is 100 km/hr.

* The speed of the conductor is 6 km/hr.

Solution:

(a). If the bus and conductor are traveling in the same direction.

The net speed of the conductor relative to the road is,

where v_1 is the velocity of the conductor relative to the road, v_b is the velocity of the bus, and v_c is the velocity of the conductor inside the bus,

Substituting the known values,

Thus, the speed of the conductor relative to the road is 106 km/hr.

(b). The speed of the conductor relative to the bus is the speed of the conductor on the bus,

Thus, the speed of the conductor relative to the bus is 6 km/hr.

Given

Resistance of the oven, R=50.0 ohm,

Voltage is V=220 V

To find

The current drawn

Explanation

Let the current be I

By Ohm's law,

Putting the values,

Conclusion

The current drawn is 4.4 A

ANSWER:

D)each block has the same kind of charge but we don't' know what kind it is

STEP-BY-STEP EXPLANATION:

Two charges of the same type always repel each other.

In this case, it is not possible to know what type of load they are, only that they are the same.

Therefore, the correct answer is:

D)each block has the same kind of charge but we don't' know what kind it is

Consider that a general way of writing a line equation is:

y = mx + b

where m is the slope of the line and b is the y coordinate of the y-intercept of the line.

Then, by using the given information:

m = 1/2

b = 7

You have the following equation of line:

y = 1/2*x + 7

Work does Scott do to push a 74 kg sofa 2.1 m across the floor at a constant speed. The coefficient of kinetic friction between the sofa and the floor is 0.23 is 349 Nm.

given that :

mass = 74 kg

distance d = 2.1 m

coefficient of kinetic friction , μk  = 0.23

work done is given as :

w = fd

f = μk m g

f = 0.23 × 74 × 9.8

f = 166 N

therefore ,

work = fd

w = 168 × 2.1

w = 349 Nm

Work does Scott do to push a 74 kg sofa 2.1 m across the floor at a constant speed. The coefficient of kinetic friction between the sofa and the floor is 0.23 is 349 Nm.

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Grant jumps 1.10 m straight up into the air to slam-dunk a basketball into the net, the speed from which he would have left the floor would be 4.64 m / s .

There are three equations of motion given by  Newton

v = u + at

S = ut + 1/2 × a × t²

v² - u² = 2 × a × s

As given in the problem grant jumps 1.10 m straight up into the air to slam-dunk a basketball into the net.

By using the third equation of the motion,

v² - u² = 2 × a × s

0 - u² = 2 × -9.81 × 1.10

u = 4.64 m / s

Thus,  the speed from which he would have left the floor would be 4.64 m / s .

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Given data:

* The mass of the sled is m_1 = 26 kg.

* The mass of the child is m_2 = 18 kg.

* The force in the upwards direction by the big brother is F_1 = 10 N.

* The force in the downwards direction by the big sister is F_2 = 16 N.

Solution:

The net mass on the sled along with the child is,

The net weight of the sled along with the child is,

The weight of the sled along the child is acting on the sled in the downwards direction.

Thus, the normal force acting on the sled (taking upward force as negative and downward force as positive) is,

Thus, the normal force acting on the sled is 437.2 N.

ANSWER:

(a)

Potential energy = 75460 J

Kinetic energy = 38500 J

Total energy = 113960 J

(b)

The site can be used to start a colony.

STEP-BY-STEP EXPLANATION:

Given:

Mass (m) = 770 kg

Velocity (v) = 10m/s

Height (h) = 10 m

(a)

We calculate in each case the kinetic and potential energy by means of their formulas

The total energy is the sum of both calculated energies:

(b)

Since the tsunami energy is less than the energy that can destroy the colony, then the site can support a permanent colony.

To find

The source of the Sun’s heat and light energy is:

Explanation

The sun's core is very hot. So under pressure nuclear fusion takes place. Here hydrogen is changed to helium.

Conclusion

The correct option is

B. fusion of hydrogen nuclei.

(a) The impulse experienced by the player is 117 Ns.

(b) The force the floor exert on the player before the jump is 637 N.

(c) The total average force exerted by the floor on the player if the player is in contact with the floor for 0.450 s during the jump is 260 N.

The impulse experienced by the player is the change in the momentum of the player.

J = ΔP

J = m(v - u)

where;

J = 65 x (0 + 1.8)

J = 117 Ns

The force the floor exert on the player before the jump is calculated as;

F = mg

where;

F = 65 x 9.8

F = 637 N

The total average force exerted by the floor on the player if the player is in contact with the floor for 0.450 s during the jump is calculated as;

F = ma

F = m(v/t)

F = (mv)/t

F = (65 x 1.8) / 0.45

F = 260 N

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Check each option to see how it relates to different concepts.

Option 1: E=hf

This equation tells the energy carried by an electromagnetic wave with frequency f.

Option 2: E=mc

This equation is not correct, since the left member is measured in units of energy and the right member does not.

Option 3: E=(1/2)mv^2

This equation relates the energy of a moving object with its mass and its velocity. It is known as kinetic energy.

Option 4: E=mc^2

Since c is a constant (the speed of light), this equation relates the energy of an object with its mass.

Therefore, the mass/energy equivalence is expressed mathematically in the equation:

For practical reasons, we can consider each side of the square as an infinite wire. This can be seen on the following drawing:

This way, the field on the center will be the sum of the contribution of each wire. We can calculate the contribution of a single wire as:

Then, the total field will be this, multiplied by the number of wires:

Then, the resulting field will be Bt=36.46uT

If you put your spoon in the microwave, nothing will happen to it as long as it has round edges and it is not touching any sides of the microwave.

Spoons are generally made from stainless steel. Stainless steels are iron and chromium. In some cases, other metals such as nickel are thrown into the mix.

Thus, being made of metals, these stainless steels are good conductors of heat and electricity.

A microwave works by heating foods put into it using electromagnetic radiation in the microwave frequency range. Electromagnetic radiation causes the molecules of food to rotate and produce thermal energy.

If the spoon touches the side of the microwave, sparks may result. Otherwise, it is totally fine because spoons usually have round edges. With rough edges,  the waves may be reflected back and forth and create sparks.

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Given,

The repulsive force exerted by the charges, F=0.500 N

The distance between the charges, d=1.5 m

From Coulomb's law,

Where q is the magnitude of the charge of each point charge and k is the coulomb's constant.

On rearranging the above equation,

On substituting the known values,

Thus the magnitude of the charge of each point charge is 1.1×10⁻⁵ C

Therefore the correct answer is option B.

The velocity of the particle at 0 s and at 1.0 and the average velocity between 0 s and 1.0

a)[tex]\vec{V}(0)=0 m / s[/tex]

[tex]\vec{V}(1)=(8 \hat{\imath}+6 \hat{k}) m / s[/tex]

b)[tex](4 \hat{\imath}+2 \hat{k}) \mathrm{m} / \mathrm{s}[/tex]

This is further explained below.

Generally, the equation for the Position is mathematically given as

F(t) = 4.01²î - 3.0ĵ +2.03 km.

Therefore

[tex]\begin{aligned}&\vec{r}(t)=\left(4 t^2 \hat{l}-3 \hat{\jmath}+2 t^3 \hat{k}\right) m \\&\vec{V}(t)=\frac{d \vec{r}(t)}{d t}=\left(8 t \hat{\imath}+6 t^2 \hat{k}\right) m / s\end{aligned}[/tex]

For A

[tex]\begin{aligned}&\vec{V}(0)=0 m / s \\&\vec{V}(1)=(8 \hat{\imath}+6 \hat{k}) m / s\end{aligned}[/tex]

For B

[tex]\text { Average velocity } &=\frac{\text { Total displacement }}{\text { time interval }} \\[/tex]

[tex]=\frac{\vec{r}(1)-\vec{r}(0)}{1} \\&=4 \hat{\imath}-3 \hat{\jmath}+2 \hat{k}-\left(-3 \hat{\jmath}^{\prime}\right) \\&=(4 \hat{\imath}+2 \hat{k}) \mathrm{m} / \mathrm{s}\end{aligned}[/tex]

In conclusion, The speed of the particle at 0 seconds and at 1.0 seconds, as well as the average speed between 0 seconds and 1.0 seconds

a)[tex]\vec{V}(0)=0 m / s[/tex]

[tex]\vec{V}(1)=(8 \hat{\imath}+6 \hat{k}) m / s[/tex]

b)[tex](4 \hat{\imath}+2 \hat{k}) \mathrm{m} / \mathrm{s}[/tex]

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the minimum force is 6 Newtons

Explanation

A moment of a force, or a torque, is a measure of a force's tendency to cause a body to rotate. The moment depends on both the force, and on the position at which the force acts, it is given by the expression

where F is the exerted force and d is the distance

Step 1

then, let

now, replace in the formula

therefore, the minimum force is 6 Newtons

I hope this helps you

Given:

The mass of the bowling ball is m1 = 1.6 kg

The mass of the pin is m2 = 0.68 kg

The initial velocity of the ball is

Required: Velocity of the bowling pin after the collision.

Explanation:

According to the conservation of momentum, the velocity after the collision will be

Final Answer: The velocity of the bowling pin after the collision is 4.21 m/s

The density of the rock sample is 3000 kg/m³.

Density is an important property of matter because it can be used to determine the weight of an object. For example, if you know the density of a rock sample and its volume, you can calculate its weight by multiplying the density by the volume. Density can also be used to determine the composition of a material. For example, if you know the densities of different materials, you can identify the material of a rock sample by measuring its density.

Density is a measure of how much mass is contained in a given volume.. The calculation of the density of the rock sample:

Density = Mass / Volume

Density = 6 kg / 0.002 m³

Density = 3000 kg/m³

As a result, the rock sample has a density of 3000 kg/m³.

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The size of the upwards force due to the water (upthrust) acting on the sphere is 12.64 N.

Buoyancy or upthrust, is an upward force exerted by a fluid on an object immersed in the fluid due to the weight of the object

Thus, upthrust is the upward force acting on an object immersed in a liquid.

Fu - Df = F(net_u)

where;

Fu - F x sin(21) = ma x sin(19)

where;

Fu -  20 x sin(21) = (4 x 4.2) x sin(19)

Fu - 7.17 = 5.47

Fu = 12.64 N

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We are asked to determine the x-coordinate of the center of mass of the given bricks. To do that, we will use the following formula:

Where:

Since we have three bricks, the formula expands to:

Since we have three bricks with the same characteristics we will assume the three of them have the same mass:

Taking "m" as a common factor and adding like terms in the denominator we get:

Now we cancel out the "m":

Now we determine the x-coordinates of each brick. Each brick is a parallelepiped, therefore, the x-coordinate is in the middle. Since each brick measures L, this means that the x-coordinate of the first brick is:

For the second brick, we have the L/2 of the separation from the first plus the L/2 of its length, therefore:

Now, for the third brick we have the L/4 of the separation from the second brick plus the L/2 of the separation of the second brick and the first brick and the L/2 of the length of the third brick, therefore:

Now we substitute in the formula for the x-coordinate:

Adding like terms in the numerator:

Simplifying:

Therefore, the x-coordinate of the center of mass is located at 11L/6 from the origin.

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ANSWER

38.34 m/s

EXPLANATION

Given:

• The mass of the coaster, m = 839 kg

• The initial height of the coaster, h = 75 m

• The acceleration due to gravity, g = 9.8 m/s²

Find:

• The final velocity of the roller coaster at the bottom of the hill, v.

The roller coaster starts from rest, so at the top of the hill, it only has gravitational potential energy and no kinetic energy. Then, at the bottom of the hill, the roller coaster is in motion, to it has kinetic energy, and, because the difference of height with the reference - which is the bottom of the hill, is zero, it has no potential energy,

By the work-energy theorem, we have the equation,

As explained above, the initial kinetic energy is 0 and the final potential energy is also 0. If we assume that there is no friction, air resistance, or other external forces, then the work done by non-conservative forces is also 0,

Replace each kind of energy with the expression to obtain them,

The mass cancels out,

Solving for v,

Replace with the known values and solve,

Hence, the velocity of the roller coaster at the bottom of the hill is 38.34 m/s, rounded to the nearest hundredth.

Take into account that this is a situation where the source moves presenting the Doppler effect.

In order to determine the wavelength of the sound generatd by the whistle at the observer, first calculate the frequency at the observer by using the following formula:

where:

f: frequency at the observer = ?

fo: source frequency = 725 Hz

vs: source speed = 25.2 m/s

v: speed of sound = 345 m/s

replace the previous values of the parameters into the fomrula for f:

Next, use the following formula to determine the wavelength of the sound at observer, by using the previous result:

Hence, the wavelength of the sound at the observer is 0.441 m

According to the given statement the band has been stretched far  is  0.25 m.

The energy that is stored when a force is used to bend an elastic object is known as elastic potential energy. Until the force is released as well as the object springs returns to its original form, doing work in the process, the energy is retained. The object may be squeezed, stretched, or bent during the deformation.

For example, if you pull a spring, it will return to its initial form when you release it (energy input equals energy output.) Elastic potential energy is rendered possible by this.

U= 1.94 J

k  = 58.7  N/m

U = 1/2 kΔ x²

1.94 = 1/2 kΔ x²

3.88/58.7 = Δ x²

x = √(3.88 /58.7)

x = 0.25 m

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ANSWER:

9340 kg*m/s

STEP-BY-STEP EXPLANATION:

Given:

Mass (m) = 934 kg

Speed (v) = 10 m/s

The formula to calculate the momentum is as follows:

The momentum of the car is 9340 kg*m/s.

Newton’s Second Law states “The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.”

Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.

Force  = mass  × acceleration

Assuming the force constant the acceleration is inversely proportional to the mass of the object.

Thus, acceleration is directly proportional to force and inversely proportional to the mass of the body.

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Given data

*The given moment of inertia is I = 3.45 kg.m^2

*The given braking torque is T = -9.40 N.m

*The angular distance traveled is

*The final angular speed is

The angular acceleration of the flywheel is calculated by using the torque and moment of inertia relation as

The formula for the initial angular speed of the flywheel is given by the rotational equation of motion as

Substitute the known values in the above expression as

Hence, the initial angular speed of the flywheel is 5.88 rad/s