Question 1

A rifle is aimed horizontally toward the center of a target 71 m away.If the bullet strikes 10 cm below the center,what was the velocity of the bullet? Note: Ignore air friction.
A) 300 m/s
B) 330 m/s
C) 500 m/s
D) 700 m/s

Accepted Answer

The answer of A rifle is aimed horizontally toward the...

Question 2

A jet airliner moving at 600 mph due east moves into a region where the wind is blowing at 120 mph in a direction 30.0° north of east.What is the new speed and direction of the aircraft?
A) 706 mph,5.67° N of E
B) 620 mph,5.67° N of E
C) 706 mph,4.87° N of E
D) 588 mph,4.87° N of E

Accepted Answer

To solve the problem, we need to use vector addition. The velocity of the plane relative to the ground can be expressed as the sum of its velocity in still air (600 mph due east) and the velocity of the wind (120 mph 30° north of east).

Using trigonometry, we can resolve the wind velocity into its components:
wind north = 120 sin 30° = 60 mph
wind east = 120 cos 30° = 103.92 mph

We can now add the velocities vectorially. Let's call the resulting velocity V.
V north = plane north + wind north = 0 + 60 = 60 mph north
V east = plane east + wind east = 600 + 103.92 = 703.92 mph east

The magnitude of V is the square root of (V north)^2 + (V east)^2 = sqrt(60^2 + 703.92^2) = 706 mph.

The direction of V can be found as the inverse tangent of (V north / V east), which gives us 4.87° north of east.

Therefore, the new speed and direction of the aircraft are 706 mph, 4.87° north of east. Answer choice C is the correct answer.

Question 3

A ball is launched from ground level at 30 m/s at an angle of 25° above the horizontal.How far does it go before it is at ground level again?
A) 14 m
B) 70 m
C) 43 m
D) 86 m

Accepted Answer

We can use the horizontal and vertical components of the velocity to solve this problem.
The initial vertical velocity is v*sin(25°) and the horizontal velocity is v*cos(25°).
When the ball is at ground level again, its vertical velocity is zero.
We can use the formula vf^2 = vi^2 + 2ad with vf = 0, vi = v*sin(25°), and a = -9.8 m/s^2.
Solving for d, we get d = vi^2 / (2a) = (30*sin(25°))^2 / (2*(-9.8)) = 70.04 m.
Therefore, the ball goes 70 m before it is at ground level again. The answer is B.

Question 4

A baseball is moving in the air along the customary parabola.Ignoring air drag,where is the force on the baseball zero?
A) at the top of the parabola
B) just when it has started upward
C) where it is about to impact
D) nowhere

Accepted Answer

The force on the baseball is never zero because gravity acts on it throughout its trajectory, including at the top of the parabola.

Question 5

Two baseballs are released at the same time.One is dropped from rest and the other is given an initial horizontal velocity.Which of the following is not true? Ignore atmospheric drag.
A) Both baseballs hit the ground at the same time.
B) Both have the same vertical component of velocity as they reach impact.
C) The horizontal component of velocity increases at a greater rate than the vertical component of velocity for both while they are both in the air.
D) The horizontally-released ball has a greater speed than the other ball for the whole trip.

Accepted Answer

The horizontal component of velocity remains constant (ignoring air resistance), while the vertical component increases due to gravity. Therefore, statement C is not true as it incorrectly suggests the horizontal component increases at a greater rate.

Question 6

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s² and air resistance is negligible,then what is the speed of the rock as it hits the ground? A) 30 m/s B) 32 m/s C) 34 m/s D) 36 m/s

Accepted Answer

The answer of A stone is thrown with an initial...

Question 7

A projectile is launched at an angle less than 30° and at speed v.Which will increase the projectile's range more,ignoring atmospheric drag?
A) doubling the launch angle
B) increasing the speed of launch by 50%
C) reducing the mass of the projectile
D) launching on February 29th

Accepted Answer

Increasing the speed of launch by 50% will significantly increase the range of the projectile. The range of a projectile is directly proportional to the square of its launch speed when launched at a fixed angle, making speed a critical factor in maximizing range. Choices A, C, and D do not directly influence the range in the same significant manner.

Question 8

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s² and air resistance is negligible,then what is the magnitude of the horizontal component of velocity as the rock strikes the ground? A) 7.5 m/s B) 9.0 m/s C) 12 m/s D) 29 m/s

Accepted Answer

Using the equations of motion, we can find the time taken for the stone to hit the ground:
S = ut + 1/2 at^2
Here, initial vertical velocity (u) = 15 sin 53° = 11.7 m/s (upwards)
a = g = 9.8 m/s^2 (downwards)
S = 40 m (height of the building)
Putting the values, we get:
40 = 11.7t - 1/2 (9.8)t^2
Solving this quadratic equation, we get t ≈ 3.67 s as the time taken.
Now, we can find the final horizontal velocity (v) using:
v = u + at
Here, initial horizontal velocity (u) = 15 cos 53° = 9.65 m/s
a = 0 (horizontal acceleration is 0)
t = 3.67 s (time taken)
Therefore,
v = u + at = 9.65 m/s + 0 × 3.67 s = 9.65 m/s

Hence, the answer is B.

Question 9

A projectile is launched with speed v at an angle θ,the angle being less than 45º.What other angle would give the same range for this projectile launched at the same speed v?
A) 2θ
B) 0.5θ
C) 90° - θ
D) 90º - 0.5θ

Accepted Answer

The range of a projectile launched at an angle θ is given by R = (v^2/g) sin(2θ), where v is the initial velocity and g is the acceleration due to gravity. To find another angle that gives the same range, we need to find an angle φ such that R = (v^2/g) sin(2φ). Solving for φ, we have sin(2φ) = sin(2θ), which gives 2φ = 180° - 2θ, or φ = (180° - 2θ)/2 = 90° - θ. So the answer is C) 90° - θ.

Question 10

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s² and air resistance is negligible,what is the magnitude of the horizontal displacement of the rock? A) 30 m B) 39 m C) 66 m D) 90 m

Accepted Answer

The answer of A stone is thrown with an initial...

Question 11

A bridge that was 8.3 m long has been washed out by the rain several days ago.How fast must a car be going to successfully jump the stream? Although the road is level on both sides of the bridge,the road on the far side is 2.0 m lower than the road on this side.
A) 5.0 m/s
B) 7.8 m/s
C) 13 m/s
D) 25 m/s

Accepted Answer

To successfully jump the stream, the car must attain a speed such that it can travel a horizontal distance of 8.3 m plus the 2.0 m height difference between the roads. Using the conservation of energy, we can equate the gravitational potential energy lost with the kinetic energy gained by the car, i.e.
(mass of car) x g x (height difference) = 0.5 x (mass of car) x (velocity)^2
Solving for velocity, we get velocity = sqrt[(2 x g x height difference)] = sqrt[(2 x 9.81 m/s^2 x 2.0 m)] = 13.0 m/s. Therefore, the best choice is C.

Question 12

A fireman,40.0 m away from a burning building,directs a stream of water from a fire hose at an angle of 30.0° above the horizontal.If the initial speed of the stream is 40.0 m/s,at what height above the nozzle will the stream of water strike the building?
A) 9.60 m
B) 16.6 m
C) 18.7 m
D) 22.4 m

Accepted Answer

The answer of A fireman,40.0 m away from a burning...

Question 13

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 14 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 7.1 s.How far out from the cliff's edge does the stone travel horizontally? Note: g = 9.8 m/s² and air resistance is negligible. A) 58 m B) 68 m C) 86 m D) 197 m

Accepted Answer

Using the kinematic equations: 
y = voy*t + 1/2*a*t^2, where y is displacement in the y direction, voy is initial velocity in the y direction, a is acceleration in the y direction (due to gravity), and t is time.

Using angle 30°, the initial velocity can be calculated as V0x = V0*cos(30°) = 12.124 m/s and V0y = V0*sin(30°) = 7 m/s.
y = V0y*t + 1/2*a*t^2
0 = 7*t - 1/2*9.8*t^2
t = 1.43 s

Using the same initial velocity, the horizontal displacement can be calculated as x = V0x*t.
x = 12.124*7.1
x = 86 m

Question 14

A baseball leaves the bat with a speed of 44.0 m/s and an angle of 30.0° above the horizontal.A 4.0-m high fence is located at a horizontal distance of 132 m from the point where the ball is struck.Assuming the ball leaves the bat 1.0 m above ground level,by how much does the ball clear the fence?
A) 18.9 m
B) 14.4 m
C) 9.8 m
D) 5.4 m

Accepted Answer

The answer of A baseball leaves the bat with a...

Question 15

A track star in the broad jump goes into the jump at 10 m/s and launches himself at 20° above the horizontal.How long is he in the air before returning to Earth? Note: g = 9.8 m/s². A) 0.35 s B) 0.42 s C) 0.70 s D) 0.89 s

Accepted Answer

We can use the kinematic equation y = yo + voy*t - 0.5*g*t^2 to find the time it takes for the track star to return to the ground.

First, we need to find the initial vertical velocity. We can use the equation voy = vo*sin(theta) = 10*sin(20°) = 3.42 m/s.

Next, we can set y = 0 (since the track star returns to the same height) and solve for t:

0 = 0 + 3.42*t - 0.5*9.8*t^2

This equation simplifies to 4.9t^2 - 3.42t = 0, which factorizes to t(4.9t - 3.42) = 0.

Taking the positive solution, we get t = 0.7 seconds. Therefore, the correct answer is C.

Question 16

Wiley Coyote has missed the elusive Road Runner once again.This time,he leaves the edge of the cliff at 40.0 m/s horizontal velocity.If the canyon is 100 m deep,how far from his starting point on the edge of the cliff does the coyote land?
A) 207 m
B) 247 m
C) 339 m
D) 400 m

Accepted Answer

The correct answer is A because the horizontal velocity is constant, so the horizontal displacement is simply the velocity multiplied by the time it takes to fall 100 m. The time it takes to fall 100 m is given by:$$t = \sqrt{\frac{2d}{g}}$$where d is the distance fallen and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get:$$t = \sqrt{\frac{2(100 \ m)}{9.8 \ m/s^2}} = 4.52 \ s$$The horizontal displacement is then:$$d = vt = (40.0 \ m/s)(4.52 \ s) = 207 \ m$$

Question 17

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s² and air resistance is negligible,then what is the magnitude of the vertical velocity component of the rock as it hits the ground? A) 30 m/s B) 24 m/s C) 26 m/s D) 29 m/s

Accepted Answer

The answer of A stone is thrown with an initial...

Question 18

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 14 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 7.1 s.What is the height of the cliff? Note: g = 9.8 m/s² and air resistance is negligible. A) 58 m B) 114 m C) 120 m D) 197 m

Accepted Answer

The answer of A stone is thrown at an angle...

Question 19

A boat moves at 11.0 m/s relative to the water.If the boat is in a river where the current is 2.00 m/s,how long does it take the boat to make a complete round trip of 1000 m upstream followed by a 1000 m trip downstream?
A) 188 s
B) 205 s
C) 208 s
D) 222 s

Accepted Answer

The answer of A boat moves at 11.0 m/s relative...

Question 20

Superguy is flying at treetop level near Paris when he sees the Eiffel Tower elevator start to fall (the cable snapped).His x-ray vision tells him Lois LaTour is inside.If Superguy is 1.00 km away from the tower,and the elevator falls from a height of 2.1 × 10² m,how long does Superguy have to save Lois,and what must be his average speed? A) 4.5 s,200 m/s B) 6.5 s,150 m/s C) 7.0 s,140 m/s D) 9.0 s,110 m/s

Accepted Answer

The answer of Superguy is flying at treetop level near...

Quiz 4: The Laws of Motion: Part A

A rifle is aimed horizontally toward the center of a target 71 m away.If the bullet strikes 10 cm below the center,what was the velocity of the bullet? Note: Ignore air friction.

A jet airliner moving at 600 mph due east moves into a region where the wind is blowing at 120 mph in a direction 30.0° north of east.What is the new speed and direction of the aircraft?

A ball is launched from ground level at 30 m/s at an angle of 25° above the horizontal.How far does it go before it is at ground level again?

A baseball is moving in the air along the customary parabola.Ignoring air drag,where is the force on the baseball zero?

Two baseballs are released at the same time.One is dropped from rest and the other is given an initial horizontal velocity.Which of the following is not true? Ignore atmospheric drag.

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s2 and air resistance is negligible,then what is the speed of the rock as it hits the ground?

A projectile is launched at an angle less than 30° and at speed v.Which will increase the projectile's range more,ignoring atmospheric drag?

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s2 and air resistance is negligible,then what is the magnitude of the horizontal component of velocity as the rock strikes the ground?

A projectile is launched with speed v at an angle θ,the angle being less than 45º.What other angle would give the same range for this projectile launched at the same speed v?

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s2 and air resistance is negligible,what is the magnitude of the horizontal displacement of the rock?

A bridge that was 8.3 m long has been washed out by the rain several days ago.How fast must a car be going to successfully jump the stream? Although the road is level on both sides of the bridge,the road on the far side is 2.0 m lower than the road on this side.

A fireman,40.0 m away from a burning building,directs a stream of water from a fire hose at an angle of 30.0° above the horizontal.If the initial speed of the stream is 40.0 m/s,at what height above the nozzle will the stream of water strike the building?

A baseball leaves the bat with a speed of 44.0 m/s and an angle of 30.0° above the horizontal.A 4.0-m high fence is located at a horizontal distance of 132 m from the point where the ball is struck.Assuming the ball leaves the bat 1.0 m above ground level,by how much does the ball clear the fence?

A track star in the broad jump goes into the jump at 10 m/s and launches himself at 20° above the horizontal.How long is he in the air before returning to Earth? Note: g = 9.8 m/s2.

Wiley Coyote has missed the elusive Road Runner once again.This time,he leaves the edge of the cliff at 40.0 m/s horizontal velocity.If the canyon is 100 m deep,how far from his starting point on the edge of the cliff does the coyote land?

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s2 and air resistance is negligible,then what is the magnitude of the vertical velocity component of the rock as it hits the ground?

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 14 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 7.1 s.What is the height of the cliff? Note: g = 9.8 m/s2 and air resistance is negligible.

A boat moves at 11.0 m/s relative to the water.If the boat is in a river where the current is 2.00 m/s,how long does it take the boat to make a complete round trip of 1000 m upstream followed by a 1000 m trip downstream?

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s² and air resistance is negligible,then what is the speed of the rock as it hits the ground?

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s² and air resistance is negligible,then what is the magnitude of the horizontal component of velocity as the rock strikes the ground?

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s² and air resistance is negligible,what is the magnitude of the horizontal displacement of the rock?

A track star in the broad jump goes into the jump at 10 m/s and launches himself at 20° above the horizontal.How long is he in the air before returning to Earth? Note: g = 9.8 m/s².

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 40-m building.If g = 9.8 m/s² and air resistance is negligible,then what is the magnitude of the vertical velocity component of the rock as it hits the ground?

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 14 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 7.1 s.What is the height of the cliff? Note: g = 9.8 m/s² and air resistance is negligible.