The magnitude of vertical component of the velocity of the plane when a ball is shot 58 m/s at 40 degree to the ground is 37.28 m/s.
What is velocity?
Velocity can be defined as the rate of change of displacement, The S.I unit of velocity is m/s.
To calculate the magnitude of the vertical component of the velocity, we use the formula below.
Formula:
Vy = Vsin∅.............. Equation 1Where:
Vy = Vertical component of the velocityV = Velocity of the ball∅ = Angle the ball makes with the groundFrom the question,
Given:
V = 58 m/s∅ = 40°Substitute these values into equation 1
Vy = 58(sin40°)Vy = 58×0.6428Vy = 37.28 m/sHence, The magnitude of the vertical component of the velocity is 37.28 m/s.
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Energy that comes from sources whose supplies are capable of being regenerated or are virtually inexhaustible is called.
Answer: Renewable
Explanation: Hope this helps.
If you are 16 miles from Charleston, how long will it take to get there if your average velocity is 42
miles per hour?
Answer:
22.9 minutes
Explanation:
Distance = Speed x Time
We want the time to go 16 miles at 42 miles/hour (mph).
16 miles = (42 mph)*T
T = 16 miles/(42 miles/hr)
Time = 0.381 hours
(60 minutes/hour)*(.381 hours)= 22.9 minutes
a marble is rolling across a flat surface with a velocity of 2 m/s. it begins to roll up a ramp. ignoring rotational kinetic energy and friction, what will be the vertical height of the marble when it comes to a stop before rolling back down?
The vertical height of the marble when it comes to a stop before rolling back is 20 centimeters.
As per the Law of conservation of energy,
If there is no external force acting on the system, the energy will always remains the same at every point of the motion.
As, we can see, there is no external force on the marble,
Energy of the marble at start will be equal to energy of the marble at the vertical height
We can write,
Energy while rolling = Energy at the highest point
1/2MV² = MgH
Where,
M is the mass of the marble,
V is the velocity of the marble,
g is the acceleration due to gravity and,
H is vertical height of the marble.
So,
1/2MV² = MgH
1/2V² = gh
Putting all the values,
1/2(2)² = 10H
H = 4/20
H = 0.2 meters.
So, the vertical height of the marble is 20 cm.
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consider newton's 3rd law, the force that the earth exerts on a person will be equal and opposite that what the person applies to the earth. however, why don't we see the earth accelerate?
According to Newton's third law, for every action there is an equal and opposite reaction. However, the land we see on earth is stationary and the force applied by us is not at all sufficient to make a movement or to accelerate.
What is Newton's third law of motion ?According to Newton's third law, for every action there is an equal and opposite reaction. Therefore, when we apply a force on an object, the object will exerts an equal and opposite force.
According to Newton's second law of motion, the force exerted on a body is the product of mass and acceleration. Hence, the force acting on body is directly proportional to the mass of the body and it accelerates by the applied force.
The mass of humans in earth is negligible compared to the mass of earth . Therefore, the force we exert on earth is not at all sufficient to accelerate the earth. However, earth in turn exerts an equal and opposite force.
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1. A vector of 15 units acts to the left, and a vector of 3 units acts to the right. What is the resultant?
Answer: 12
Explanation:
The resultant vector is 12 unit.
What is addition of two vector?When two vectors point in the same direction, their sum is equal to the total of their respective magnitudes pointing in the same direction.
When two vectors are pointed in opposite directions, the resultant vector is pointed in the direction of the larger vector and is equal to the difference between their magnitudes.
Here, one vector of 15 unit is acting to the left and another vector of 3 unit acting rightwards. As they are acting in opposite direction, vector summation of two vector will be equal to the value of subs traction of their magnitude.
So, Resultant vector= 15 unit + (-3 unit)
= 15 unit - 3 unit
= 12 unit.
Hence, the resultant vector will be 12 unit.
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What is your total displacement if you walk 30m East and 50m North?
The total displacement would be 110m.
The total distance is 50 m + 30 m + 30 m = 110 m. The displacement is the shortest route from the starting point. It is solved using vectors.
What is Displacement?
Displacement is a vector quantity which depends on the direction of motion but distance is a scalar quantity which just sums up all the given quantity values. The displacement is simply the difference between the locations of the two markers and is unrelated to the route used to get there. It is a vector quantity that has a direction and magnitude.
Hence, the total displacement if you walk 30m East and 50m North would be 110m.
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Answer:
58.31 meters northeast
Explanation:
The displacement can be modeled into the vector equation of [tex]\displaystyle{\vec s = 30\hat x + 50\hat y}[/tex]. We can find the magnitude of displacement by applying Pythagoras Theorem. Suppose we have a two-dimensional vector equation [tex]\displaystyle{\vec v = a\hat x + b\hat y}[/tex] then the magnitude of vector is [tex]\displaystyle{|\vec v\, | = \sqrt{a^2+b^2}}[/tex].
Therefore, the magnitude of displacement is:
[tex]\displaystyle{|\vec s\, | = \sqrt{30^2+50^2}}\\\\\displaystyle{=\sqrt{900+2500}}\\\\\displaystyle{=\sqrt{3400}}\\\\\displaystyle{\approx 58.31 \ \sf m}[/tex]
Since 30 meters east and 50 meters north form northeast direction then the displacement is 58.31 meters northeast.
How much gravitational force is acting on a 5 kg bowling ball resting on the floor?
A. 0.2 N
B. 9.8 N
C. 1 N
D. 49 N
Answer:
Explanation:
F = m * a = 5 kg * 9.81 m/s^2 = ~ 49 N
Scripture Spotlight: Proverbs 6:6-11
the term sluggard comes from slugs, which move like snails, s-l-o-w-l-y. What is the message of the above passage? Read it in several Bible versions
Answer: A sluggard is someone who is habitually lazy or inactive. Such a person does not take personal responsibility for his own life. The word sluggard is used 14 times in the book of Proverbs. In each case, the Bible condemns laziness and warns of the consequences of being a sluggard.
Proverbs 6:9 asks two rhetorical questions, highlighting one of the main traits of a sluggard: “How long will you lie there, you sluggard? / When will you get up from your sleep?” Verse 6 tells the sluggard to learn a lesson from an industrious insect: “Go to the ant, you sluggard; / consider its ways and be wise!”
Explanation:
a 6.0-kg fish swimming 1.1 m/s swallows an absentminded 1.0-kg fish swimming toward it at a speed that brings both fish to a halt immediately after lunch. find the speed of the approaching smaller fish before lunch.
The speed of the approaching smaller fish before lunch is 6m/s.
What is the speed?The entire distance that an object travels in a predetermined amount of time is the definition of speed.
Given that the speed v₁ of big fish is 1 m/s and mass m₁ is 6kg. The mass m₂ of small fish is 1 kg.
Both fish have linear momentum of,
p₁ = m₁v₁ + m₂v₂
Where,
p₁ is the initial linear momentum
v₂ is the speed of the small fish.
Since both fish are traveling in the same direction and v is their ultimate meeting velocity, the final linear momentum will be given as,
p₂ = (m₁ + m₂) v
Linear momentum is held constant hence,
p₁ = p₂
m₁v₁ + m₂v₂ = (m₁ + m₂) v
The fish's final speed will be zero because they stopped moving., so
m₁v₁ + m₂v₂ = 0
v₂ = - m₁v₁/m₂
v₂ = -6×1/1
v₂ = -6
The negative symbol indicates that the tiny fish are swimming against the current.
The speed of the approaching smaller fish before lunch is 6m/s.
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If the same elevator accelerates downwards
with an acceleration of 1.2 m/s
2
, what is the
upward force exerted by the elevator floor on
the passenger?
The upward force exerted by the elevator floor on the passenger is 7.6 times mass of the passenger.
What is force?A force in physics is an effect that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Given in question elevator accelerates downwards with an acceleration of 1.2 m/s². There is acceleration due to gravity working downward which is 9.8 m/s².
So, net acceleration due to gravity is given as 9.8 - 1.2 = 7.6 m/s²
The upward force exerted by the elevator floor on the passenger is mass times acceleration, 7.6 times mass of passenger.
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two circuits present the same resistance to the cu rrent. in one circuit the battery causing the flow of current has a voltage of 9.0 v, and the current is 3.0 a. in the other circuit the battery has a voltage of 1.5 v. what is the current in this other circu it?
The current in this other circuit while the time remains constant, the current is doubled and the resistance is cut in half.
According to Ohm's law, the resistance (R) in a circuit has an inverse relationship to the electrical current (I), which is proportional to the voltage (V) (R). Therefore, if the voltage is raised, the current will rise as long as the circuit's resistance remains constant. Ohm's Law describes the relationship between current, voltage, and resistance. This states that, provided the temperature stays constant, the current flowing in a circuit is directly proportional to the applied voltage and inversely proportional to the circuit resistance. As long as the resistance is kept constant, an increase in voltage will therefore result in an increase in current.
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in general, what is true about the frequency at which an object vibrates? multiple choice question. the slower the vibrations, the softer the sound the slower the vibrations, the higher the pitch the faster the vibrations, the louder the sound produced the faster the vibrations, the higher the pitch
The statement that is true concerning the frequency include the following: slower the vibrations, the softer the sound, the faster the vibrations, the louder the sound produced and the faster the vibrations, the higher the pitch. That is option A,C and D.
What is sound?Sound is defined as the type of wave that is being created when disturbance causes vibration through a medium such as water, air or solid medium.
The properties of a sound wave include the following:
Frequency,Pitch,Wavelength andAmplitude.The frequency of the sound wave is affects other properties which is the number of sound waves a sound produces per second.
A low frequency would lead to low sound and pitch production while a high frequency would lead to a high sound and pitch production.
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1.A 98.0 kg basketball player runs at a speed of 7.0 m/s. What is KE?
2.A jogger whose mass is 65 kg is moving at a speed of 4 m/s. What is the jogger's KE?
Answer:
Brainliest Answer?
2401J 520JExplanation:
E = ( 1 / 2 )mv²
b = ( 1 / 2 )( 98kg )( 7ms⁻¹ )²
b = ( 49 )²kgm²s⁻²
b = 2401J
j = ( 1 / 2 )( 65kg )( 4ms⁻¹ )²
j = ( 1 / 2 )( 65kg )( 16m²s⁻² )
j = 520kgm²s⁻²
j = 520J
Answer:
Explanation:
Given:
m = 98.0 kg
V = 7.0 m/s
__________
Ek - ?
KE - kinetic energy
Ek = m·V² / 2
Ek = 98.0*7.0² / 2 ≈ 2 400 J
Neptune has a mass that is about 17 times the mass of earth. the distance between the sun and neptune is about 30.1 times the distance between the sun and earth. if the gravitational force between the sun and earth is 3.5 x 1028 n, which is closest to the force between neptune and the sun? 6 x n 6 x n 6 x n 6 x n
We would weigh 114 kg on Neptune if we weighed 100 kg on Earth. In comparison, we would experience much lower gravity on the Moon (16.5%) or Mars (37.6%).
Neptune is much larger than Earth. In fact, its mass is 17 times that of the Earth. Neptune's surface gravity is approximately 110% that of Earth's, so if you weigh 100 pounds on Earth, you would weigh 110 pounds on Neptune (assuming you could find someplace to, well, stand). M is subdivided into two parts, m1 and m2. The ratio of m1/M for which the gravitational attraction between the two parts becomes maximum at a given separation is. 1:1.
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Answer:
6 x 10^26 N
Explanation:
What is the weight of a boy with a mass of 50 kg on Earth?
Use g= 9.81 m/s² and do not include units in your answer.
Answer:
490.5
Explanation:
Force = Mass × Acceleration
Since, Weight is a force and 'g' is the acceleration due to the earth's gravity,
Weight = Mass × g
Weight = 50 kg × 9.81 m/s² = 490.5 kg-m/s² or 490.5 N
Consider a planet orbiting a sun-like star that has been detected by the doppler and that has an orbital period of one year. The larger the velocity changes measured for the star, the __________.
The larger the velocity changes measured for the planet, the larger will be the mass of the star and smaller will be the orbit's radius.
v = √ ( G M / r )
v = Orbital velocity
G = Gravitational constant
M = Mass of the central body
r = Radius of orbit
v ∝ √ M
v ∝ 1 / √ r
From the above equation is is clear that velocity of the planet increases with the increase of star's mass and increases with the decrease of planet's orbital radius.
Therefore, the larger the velocity changes measured for the star, the larger will be the mass of the star and smaller will be the orbit's radius.
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A manufacturer of echo effects for music recording studios has built a prototype of an echo device that sounds exactly like a beloved echo machine from the 1970s. even though its computer chips are cheap, they are hard to find because the compounds originally used to make the chips are no longer being manufactured. what type of issue does the effects manufacturer need to overcome in order to be able to mass produce this echo device? availability cost effectiveness safety time effectiveness
Since sound expands and loses intensity as it moves farther away, the echo is weaker than the initial sound and has a smaller amplitude. For instance, when a speaker's voice is heard and its echo is compared.
One kind of audio effect that involves gradually delaying a signal is an echo effect. In this instance, after some amount of time, listeners hear the same signal repeated audibly. When the time delay is relatively long (more than 30 milliseconds), listeners can distinguish between the echoes.
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Answer:
D: Availability
Explanation:
correct on edge 2023
OPEN ENDED QUESTION
The skater eventually comes to a stop.
What has happened to all of the skater's
original potential energy?( this is on the Ed puzzle skate park please help I’m about to cry
Answer:
The maximum amount of kinetic energy the skateboarder can have is entirely dependent on the amount of potential energy of the system.
Explanation:
As the skateboarder moves, her potential energy is converted to kinetic energy (KE), or the energy of motion as her position changes along the track and the velocity changes.
Answer:
Explanation:
Kinetic energy turned into internal energy.
Potential energy has not changed.
during keon's golf drive, the angular velocity of his club is zero at the top of the backswing and 33 rad/s at the bottom of the downswing just before ball impact. the downswing lasts 0.29 s, and the distance from the club head to the axis of rotation is 1.88 m at the bottom of the downswing. what is the average tangential acceleration of the club during the downswing (in m/s2)?
The average tangential acceleration of the club during the downswing is 113.79 rad/s².
Centripetal acceleration is due to the change within the direction of tangential speed, whereas tangential acceleration is due to any trade inside the value of the tangential speed.
The tangential acceleration is while the rotational velocity adjustments, that is 0 for uniform circular motion. while vector speed adjustments path however not important. for this reason Tangential acceleration =zero. Angular acceleration is the trade in angular velocity divided by using time, whilst tangential acceleration is the change in linear speed divided through time.
given,
∆ ω = 33 rad/s
∆t = 0.29 sec
α = (change in ω)/(change in t)
α = 33 rad/s / 0.29 s = 113.79 rad/s²
tangential acceleration = r α = 1.88*113.79 = 213.93 m/s2
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Efficiency of Machines Quick Check
Which is the equation for a machine's efficiency? (1 point)
O Efficiency
O Efficiency input energy - output energy
input energy . 100
=
=
=
output energy
input energy
O Efficiency output energy
O Efficiency input energy + output energy
=
. 100
The equation for a machine's efficiency is Efficiency = Output energy / Input energy * 100
Efficiency = ( Output energy / Input energy ) * 100
The efficiency of an ideal machine is 100% where Output energy is equal to Input energy. The efficiency cannot be greater than 100% in any machine. Because work done by the machine cannot be more than the work done on the machine.
The efficiency of a machine in real world is always less than 1 because some of the input energy is lost as friction or heat in any type of machine. So the ideal machine is possible in real world applications.
Therefore, the equation for a machine's efficiency is Efficiency = Output energy / Input energy * 100
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a projectile with a mass of 20 grams is launched with a horizontal linear momentum of 15000 g cm/s; after it falls 250 cm vertically what would be its horizontal displacement? assume horizontal velocity remains constant after launch.
The horizontal displacement of the projectile is determined as 5.3 m.
What is the horizontal displacement of the projectile?The horizontal displacement of the projectile is calculated using the following equation.
X = vt
where;'
v is the horizontal velocity if the projectilet is the time of motionThe time of motion of the projectile is calculated as follows;
t = √(2h/g)
where;
h is the height of fall of the projectile = 250 cm = 2.5 mg is acceleration due to gravityt = √(2 x 2.5 / 9.8)
t = 0.71 s
The horizontal velocity of the projectile is calculated as follows;
P = mv
where;
P is momentum of the projectilem is massv is horizontal velocityv = P/m
v = (15000 g cm/s) / (20 g)
v = 750 cm/s = 7.5 m/s
X = 7.5 x 0.71
X = 5.3 m
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Describe and explain a danger to a driver of not wearing a safety belt during a sudden stop.
6. A ball rolls off a table and falls 0.75 m to the floor, landing with a speed of 4.0 m/s. 1. What is the acceleration of the ball just before it strikes the ground? 2. What was the initial speed of the ball? 3. What initial speed must the ball have if it is to land with a speed of 5.0 m/s?
1 ) Acceleration of the ball just before it strikes the ground = 10.67 m/s²
2 ) The initial speed of the ball = 1.15 m / s
3 ) The initial speed of the ball if the ball lands at 5.0 m/s = 3.2 m / s
v² = u² + 2 a s
v = Final velocity
u = Initial velocity
a = Acceleration
s = Displacement
1 ) In vertical motion,
v = 4 m / s
s = 0.75 m
u = 0
4² = 0 + ( 2 * a * 0.75 )
a = 16 / 1.5
a = 10.67 m / s²
2 ) The initial speed of the ball,
Resolving the velocity into its horizontal and vertical components,
[tex]V_{y}[/tex]² = [tex]U_{y}[/tex]² + 2 a s
[tex]V_{y}[/tex]² = 0 + ( 2 * 9.8 * 0.75 )
[tex]V_{y}[/tex] = 3.83 m / s²
V² = [tex]V_{x}[/tex]² + [tex]V_{y}[/tex]²
4² = [tex]V_{x}[/tex]² + 3.83²
[tex]V_{x}[/tex] = √ 16 - 14.67
[tex]V_{x}[/tex] = 1.15 m / s
[tex]V_{x}[/tex] = [tex]U_{x}[/tex] = 1.15 m / s
3 ) If the ball lands with a speed of 5.0 m/s,
V² = [tex]V_{x}[/tex]² + [tex]V_{y}[/tex]²
5² = [tex]V_{x}[/tex]² + 3.83²
[tex]V_{x}[/tex] = √ 25 - 14.67
[tex]V_{x}[/tex] = 3.2 m / s
[tex]V_{x}[/tex] = [tex]U_{x}[/tex] = 3.2 m / s
Therefore,
1 ) Acceleration of the ball just before it strikes the ground = 10.67 m/s²
2 ) The initial speed of the ball = 1.15 m / s
3 ) The initial speed of the ball if the ball lands at 5.0 m/s = 3.2 m / s
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A car with a weight of 6996 N is subjected to a net force of 1.74e4. The cars acceleration will be
Answer: 24.37 m/s/s [forward] = a
Explanation:
First, find mass with the Fgrav formula.
Fgrav=mg
6996=m(9.8)
713.88 kg
Then, plug the answer into Newton's second law formula.
Fnet = ma
1.74e4 = (713.88)a
(1.74e4)/(713.88) = a
24.37 m/s^2 = a
if a 3.0 kg toy is moving at 4.0 m/s then what would be kentic energy of the cart is moving twice as faster
It tells us that a toy has a mass of 3.0 kg, with a speed of 4.0 m/s.
We apply the following formula:
Ec = m * v²/2
We replace data and solve:
Ec = 3.0 kg* (4.0 m/s)²
Ec = 3.0 kg* 16 m²/s²/2
Ec = 48 kg * m²/s²/2
Ec = 24 kg * m²/s²
Ec = 24 N * m ========> Joules units
Ec = 24 J
The new cartia of the cart would be of 24 joules.testing of a light switch is being discussed. technician a says a switch can be tested with a voltmeter. technician b says to use a fused jumper wire to see if the switch is operating. who is correct?
Both technician are correct .
What is voltmeter ?
A voltmeter, also known as a voltmeter, is an instrument used to measure the potential difference or voltage between two points in an electrical or electronic circuit. Some voltmeters are intended for use on direct current (DC) circuits. Others are designed for AC circuits. A dedicated voltmeter can measure radio frequency (RF) voltage.
A simple analog voltmeter consists of a sensitive galvanometer (ammeter) in series with a high resistance. The internal resistance should be high inside . Otherwise, significant currents will flow and interfere with the operation of the circuit under test. The sensitivity of the galvanometer and the value of the series resistance determine the range of voltages the meter can display.
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Air pressure increases as you travel higher above sea level. This is the reason that cabins in commercial airliners require pressurization.
True
False
The answer is true about the cabins in commercial airliners that require pressurization.
Why are the cabins of commercial airplanes pressurized?Airplanes are pressurized because the air is very thin at the high altitude where they fly. The passenger jet has a cruising altitude of about 30,000 - 40,000 feet. At this altitude or height, humans can't breathe very well and our body gets less amount of oxygen. Most aircraft cabins are pressurized to an altitude about 8,000 feet. This is called cabin altitude. Aircraft pilots have access to the control's mode of a cabin pressure control system and if needed it can command the cabin to depressurize.
So we can conclude that cabins in commercial airliners require pressurization because of the greater pressure of the surrounding environment.
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(1 point) suppose a spring with spring constant 8 n/m is horizontal and has one end attached to a wall and the other end attached to a mass. you want to use the spring to weigh items. you put the spring into motion and find the frequency to be 0.9 hz (cycles per second). what is the mass? assume there is no friction. mass
According to the given statement The mass attached to the spring is 3.99 kg.
What is Spring mass system ?A spring system with a block hanging from or affixed to the spring's free end is known as a spring-mass system. The spring-mass system is typically used to calculate the duration of any object in a simple harmonic motion.
Briefing:F = -kx
where k is the spring constant, and
x is the displacement of the spring
The angular frequency of the spring is:
[tex]\omega=\sqrt{\frac{k}{m}}[/tex]
m is the mass of object attached to the spring
So, frequency:
f = ω/2π = [tex]\frac{1}{2 \pi} \sqrt{\frac{k}{m}}[/tex]
m = 4π²f² / k
given that f = 0.9 Hz, and
k = 9 N/m
m = (4×π²×0.9²)/8
m = 3.99 kg
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Forces with magnitudes of v = 135 newtons and u = 280 newtons act on a hook (see figure). The angle between the two forces is 45°. Find the direction and magnitude of the resultant of these forces. (Hint: Write the vector representing each force in component form, then add the vectors. Round your answers to two decimal places.)
To find the resultant force we will first find the component force of the forces given, to do this, we need to remember that any vector can be express in component form by:
[tex]\begin{gathered} \vec{v}= \\ \text{ where } \\ v\text{ is the magnitude } \\ \theta\text{ is the angle of the vector with respect to the positive x-axis.} \end{gathered}[/tex]For force u we notice that its magnitude is 280 N and its angle is zero, then we have:
[tex]\begin{gathered} \vec{u}=<280\cos0,280\sin0> \\ \vec{u}=<280,0> \end{gathered}[/tex]For force v we know that its magnitude is 135 N and its angle is 45°, then we have:
[tex]\begin{gathered} \vec{v}=<135\cos45,135\sin45> \\ \vec{v}=<95.46,95.46> \end{gathered}[/tex]Now that we have both vectors in component form we add them to get the resultant in component form:
[tex]\begin{gathered} \vec{F}=\vec{u}+\vec{v} \\ \vec{F}=<280,0>+<95.46,95.46> \\ \vec{F}=<375.46,95.46> \end{gathered}[/tex]Once we have the resultant force in component form we can find its magnitude and direction if we remember that they are given by:
[tex]\begin{gathered} F=\sqrt{F_x+F_y} \\ \theta=\tan^{-1}(\frac{F_y}{F_x}) \end{gathered}[/tex]Plugging the values we found for the components we have:
[tex]\begin{gathered} F=\sqrt{375.46^2+95.46^2} \\ F=387.41 \end{gathered}[/tex]and
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{95.46}{375.46}) \\ \theta=14.27 \end{gathered}[/tex]Therefore, the magnitude of the resultant force is 387.41 N and the direction is 14.27°
As shown in the diagram below, a soccer player kicks a ball directly toward the goal along a displacement vector r, which has a length of 7.7 m and a direction 30 degrees east of south. Alternatively, she could have kicked it to a second player standing directly in front of the goal along a displacement ry, who could have then kicked it to the goal along a displacement vector rx, as shown. Find the magnitudes (in m) and directions of rx and ry
Given that, the soccer player makes a displacement r = 7.7 m from the goal.
The distance between this player and the second player is [tex]r_{y}[/tex], and the distance between the second player and the goal is [tex]r_{x}[/tex]. The angle made by the first player with the goal is θ = [tex]30^{0}[/tex] east of south.
The magnitudes of [tex]r_{x}[/tex] and [tex]r_{y}[/tex] can be determined using the trigonometric rules.
r is the hypotenuse of the triangle formed (as shown in figure in the question), and [tex]r_{x}[/tex] is the side of triangle which is opposite to the angle θ = [tex]30^{0}[/tex]. So, [tex]r_{x}[/tex] = r sinθ = 7.7m × sin(30°) = 3.85 m.
[tex]r_{y}[/tex] is the side of triangle adjacent to the angle θ = [tex]30^{0}[/tex]. So, [tex]r_{y}[/tex] = r cosθ = 7.7m × cos(30°) = 5.445 m.
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