Question 1

The horizontal and vertical components of the initial velocity of a football are 16 m/s and 20 m/s respectively. How long does it take for the football to rise to the highest point of its trajectory?
A) 1.0 s
B) 2.0 s
C) 3.0 s
D) 4.0 s
E) 5.0 s

Accepted Answer

To find the time taken for the football to rise to its highest point, we need to use the fact that the vertical velocity at the highest point is 0 m/s. We know that the initial vertical velocity is 20 m/s, and due to gravity, the vertical velocity decreases at a rate of 9.8 m/s^2. Therefore, we can use the following kinematic equation to find the time taken:

vf = vi + at

where 
vf = final velocity (0 m/s) 
vi = initial velocity (20 m/s) 
a = acceleration (-9.8 m/s^2) 
t = time

0 = 20 - 9.8t

9.8t = 20

t = 20/9.8 ≈ 2.04 s

Therefore, the football takes about 2.0 seconds to rise to the highest point of its trajectory. The best answer choice is B.

Question 2

A projectile is fired from ground level with an initial speed of 55.6 m/s at an angle of 41.2° above the horizontal.
(a) Determine the time necessary for the projectile to reach its maximum height.
(b) Determine the maximum height reached by the projectile.
(c) Determine the horizontal and vertical components of the velocity vector at the maximum height.
(d) Determine the horizontal and vertical components of the acceleration vector at the maximum height.

Accepted Answer

The answer of A projectile is fired from ground level...

Question 3

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. What is the initial velocity of the bullet? A) 86.6 m/s B) 50.0 m/s C) 36.6 m/s D) 100 m/s E) 136 m/s

Accepted Answer

The initial velocity of the bullet can be found using the Pythagorean theorem: v = √(vx² + vy²) = √(86.6² + 50.0²) = 100 m/s.

Question 4

A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angle of 20° above the horizontal. How long is the jumper in the air before returning to the Earth?
A) 0.21 s
B) 0.42 s
C) 0.84 s
D) 1.3 s
E) 1.6 s

Accepted Answer

First, we need to find the initial vertical and horizontal components of the velocity.

Vertical: 
v_y = v*sin(20°) = 12*sin(20°) = 4.09 m/s

Horizontal: 
v_x = v*cos(20°) = 12*cos(20°) = 11.01 m/s

Next, we can use the vertical component to find the time of flight:

v_y = gt/2 
4.09 = 9.81*t/2 
t = (2*4.09)/9.81 = 0.84 s

Therefore, the jumper is in the air for 0.84 seconds before returning to the Earth.

Question 5

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.00 m. How far from the edge of the table, measured along the floor, does the puck hit the floor?
A) 20.0 m
B) 40.0 m
C) 12.8 m
D) 19.6 m
E) 6.4 m

Accepted Answer

The puck has an initial vertical velocity of 0 m/s and an initial horizontal velocity of 20.0 m/s. The time it takes for the puck to hit the floor is:$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2(2.00 	ext{ m})}{9.81 	ext{ m/s}^2}} = 0.636 	ext{ s}$$The horizontal distance the puck travels before hitting the floor is:$$d = vt = (20.0 	ext{ m/s})(0.636 	ext{ s}) = 12.8 	ext{ m}$$

Question 6

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. At what angle is the bullet fired above the horizontal? A) 45.0° B) 60.0° C) 30.0° D) 90.0° E) 75.0°

Accepted Answer

We know that the initial x- and y-components of velocity are given by:

Vx = 86.6 m/s
Vy = 50.0 m/s

The angle above the horizontal at which the bullet is fired is given by:

θ = tan^-1(Vy/Vx)

θ = tan^-1(50.0/86.6)

θ ≈ 30.0°

Therefore, the best choice is C) 30.0°.

Question 7

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long does it take before the bullet gets to the highest point of its trajectory? A) 5.0 seconds B) 10.0 seconds C) 15.0 seconds D) 20.0 seconds E) None of the other choices is correct.

Accepted Answer

To determine the time it takes for the bullet to reach the highest point of its trajectory, we need to first find the vertical component of its velocity at that point, as this will be zero. Using the formula v_fy = v_iy + gt, where v_fy is the final vertical velocity (which is 0 at the highest point), v_iy is the initial vertical velocity (which is 50.0 m/s at the start), g is the acceleration due to gravity (10.0 m/s^2), and t is the time it takes to reach the highest point, we can solve for t:

0 = 50.0 m/s - 10.0 m/s^2 * t
t = 5.0 seconds

Therefore, it takes 5.0 seconds for the bullet to reach the highest point of its trajectory. The answer is (A).

Question 8

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.0 m. What is the magnitude of the vertical component of the velocity of the puck just before it hits the ground?
A) 20.0 m/s
B) 6.26 m/s
C) 12.5 m/s
D) 19.6 m/s
E) 21 m/s

Accepted Answer

The motion of the puck can be analyzed using the equations of motion under constant acceleration due to gravity. The horizontal component of the velocity remains constant (20.0 m/s), while the vertical component experiences a constant acceleration of 9.8 m/s^2 downwards. Using the equation vf^2 = vi^2 + 2ad, where vf is final velocity, vi is initial velocity, a is acceleration, and d is displacement, we can calculate the final velocity of the puck just before it hits the ground:

vf^2 = vi^2 + 2ad
vf^2 = 0 + 2(9.8 m/s^2)(2.0 m)
vf = 6.26 m/s

Therefore, the magnitude of the vertical component of the velocity of the puck just before it hits the ground is approximately 6.26 m/s.

Question 9

A hockey puck slides off the edge of a table with an initial velocity of 28.0 m/s. The height of the table above the ground is 2.00 m. What is the angle below the horizontal of the velocity of the puck just before it hits the ground?
A) 77.2°
B) 72.6°
C) 12.8°
D) 12.6°
E) 31.8°

Accepted Answer

The answer of A hockey puck slides off the edge...

Question 10

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. What is the range of the bullet? A) 500 m B) 1000 m C) 100 m D) 866 m E) 433 m

Accepted Answer

The answer of A bullet is fired with a certain...

Question 11

A ball rolls over the edge of a table with a horizontal velocity v m/s. The height of the table is 1.6 m and the horizontal range of the ball from the base of the table is 20 m. What is the horizontal velocity of the ball just before it touches the ground?
A) 35 m/s
B) 9.8 m/s
C) 20 m/s
D) 4.9 m/s
E) 70 m/s

Accepted Answer

Explanation:Using the equation of motion, v^2 = u^2 + 2as, we have:v^2 = 0 + 2 * 9.8 * 1.6v^2 = 31.36v = 5.6 m/sThe horizontal velocity of the ball just before it touches the ground is equal to its initial horizontal velocity, which is 5.6 m/s.

Question 12

A ball rolls over the edge of a table with a horizontal velocity v m/s. The height of the table is 1.6 m and the horizontal range of the ball from the base of the table is 20 m. What is the initial speed of the ball?
A) 9.8 m/s
B) 20 m/s
C) 35 m/s
D) 4.9 m/s
E) 70 m/s

Accepted Answer

Using the kinematic equations, we can solve for the initial speed of the ball:
y = 1.6 m (height of table)
x = 20 m (range)
g = 9.8 m/s^2 (acceleration due to gravity)

y = vi*t + 1/2*g*t^2   (where t is the time it takes for the ball to hit the ground)
x = v*t
t = x/v

Substituting:
1.6 = vi*x/v + 1/2*g*(x/v)^2
1.6v^2 = vi*x*v + 1/2*g*x^2
vi = (1/2*g*x^2)/(x*v) + v

Simplifying:
vi = x/2*(g*v^2+x^2)^(1/2) + v

Plugging in the given values:
vi = 20/2*(9.8*v^2+20^2)^(1/2) + v
vi = 35.1 m/s

Therefore, the initial speed of the ball was 35 m/s.

Question 13

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.0 m. What is the magnitude of the velocity of the puck just before it touches the ground?
A) 21 m/s
B) 22 m/s
C) 24 m/s
D) 25 m/s
E) 6.3 m/s

Accepted Answer

The answer of A hockey puck slides off the edge...

Question 14

A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angle of 20° above the horizontal. How far does the jumper jump?
A) 3.4 m
B) 6.2 m
C) 9.4 m
D) 15 m
E) 18 m

Accepted Answer

To solve the problem, we can use the equation for the horizontal range of a projectile:

Range = (v^2/g) * sin(2θ)

where v is the initial speed, g is the acceleration due to gravity, and θ is the launch angle.

Plugging in the given values, we get:

Range = (12^2/9.81) * sin(2*20°) ≈ 9.4 m

Therefore, the answer is C) 9.4 m.

Question 15

A ball rolls off the edge of a table with an initial velocity of 20 m/s. The height of the table above the ground is 2.0 m. How long does it take the ball to reach the ground?
A) 0.49 s
B) 0.98 s
C) 0.64 s
D) 2.0 s
E) 0.32 s

Accepted Answer

The answer of A ball rolls off the edge of...

Question 16

A ball rolls over the edge of a table with a horizontal velocity v m/s. The height of the table is 1.6 m and the horizontal range of the ball from the base of the table is 20 m. How long does it take for the ball to hit the ground?
A) 0.29 s
B) 0.57 s
C) 1.14 s
D) 2.0 s
E) 9.8 s

Accepted Answer

The answer of A ball rolls over the edge of...

Question 17

A ball is thrown horizontally with an initial velocity of 40 m/s from a height of 10 m. How long will it take for the ball to touch the ground? Use g = 10 m/s². A) 0.70 second B) 1.0 second C) 2.0 seconds D) 1.4 seconds E) 2.4 seconds

Accepted Answer

We can solve for the time by using the kinematic equation:
y = ut + 1/2at^2
where y = 10 m (initial height), u = 0 (horizontal initial velocity), a = g = 10 m/s^2,
and t = time

Solving for t, we get:
10 = 0(t) + 1/2(10)(t^2)
t^2 = 2
t = √2 ≈ 1.4 seconds

Therefore, the answer is D) 1.4 seconds.

Question 18

The horizontal and vertical components of the initial velocity of a football are 24 m/s and 7 m/s respectively. What is the initial velocity of the football?
A) 31 m/s
B) 25 m/s
C) 17 m/s
D) 42 m/s
E) 625 m/s

Accepted Answer

The initial velocity can be found using the Pythagorean theorem: √(24² + 7²) = √(576 + 49) = √625 = 25 m/s.

Question 19

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long does it take before the bullet hits the ground? A) 5.0 seconds B) 10.0 seconds C) 15.0 seconds D) 20.0 seconds E) None of the other choices is correct.

Accepted Answer

The time of flight for a projectile is given by $ t = \frac{2v_{y0}}{g} $. Substituting $ v_{y0} = 50.0 \, \text{m/s} $ and $ g = 10.0 \, \text{m/s}^2 $, we get $ t = \frac{2 \times 50.0}{10.0} = 10.0 \, \text{seconds} $.

Question 20

A projectile is shot horizontally at 23.4 m/s from the roof of a building 55.0 m tall.
(a) Determine the time necessary for the projectile to reach the ground below.
(b) Determine the distance from the base of the building that the projectile lands.
(c) Determine the horizontal and vertical components of the velocity just before the projectile reaches the ground.

Accepted Answer

The answer of A projectile is shot horizontally at 23.4...

Quiz 4: Two-Dimensional Kinematics

The horizontal and vertical components of the initial velocity of a football are 16 m/s and 20 m/s respectively. How long does it take for the football to rise to the highest point of its trajectory?

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s2. The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. What is the initial velocity of the bullet?

A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angle of 20° above the horizontal. How long is the jumper in the air before returning to the Earth?

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.00 m. How far from the edge of the table, measured along the floor, does the puck hit the floor?

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s2. The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. At what angle is the bullet fired above the horizontal?

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long does it take before the bullet gets to the highest point of its trajectory?

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.0 m. What is the magnitude of the vertical component of the velocity of the puck just before it hits the ground?

A hockey puck slides off the edge of a table with an initial velocity of 28.0 m/s. The height of the table above the ground is 2.00 m. What is the angle below the horizontal of the velocity of the puck just before it hits the ground?

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s2. The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. What is the range of the bullet?

A ball rolls over the edge of a table with a horizontal velocity v m/s. The height of the table is 1.6 m and the horizontal range of the ball from the base of the table is 20 m. What is the horizontal velocity of the ball just before it touches the ground?

A ball rolls over the edge of a table with a horizontal velocity v m/s. The height of the table is 1.6 m and the horizontal range of the ball from the base of the table is 20 m. What is the initial speed of the ball?

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.0 m. What is the magnitude of the velocity of the puck just before it touches the ground?

A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angle of 20° above the horizontal. How far does the jumper jump?

A ball rolls off the edge of a table with an initial velocity of 20 m/s. The height of the table above the ground is 2.0 m. How long does it take the ball to reach the ground?

A ball rolls over the edge of a table with a horizontal velocity v m/s. The height of the table is 1.6 m and the horizontal range of the ball from the base of the table is 20 m. How long does it take for the ball to hit the ground?

A ball is thrown horizontally with an initial velocity of 40 m/s from a height of 10 m. How long will it take for the ball to touch the ground? Use g = 10 m/s2.

The horizontal and vertical components of the initial velocity of a football are 24 m/s and 7 m/s respectively. What is the initial velocity of the football?

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s2. The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long does it take before the bullet hits the ground?

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. What is the initial velocity of the bullet?

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. At what angle is the bullet fired above the horizontal?

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long does it take before the bullet gets to the highest point of its trajectory?

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. What is the range of the bullet?

A ball is thrown horizontally with an initial velocity of 40 m/s from a height of 10 m. How long will it take for the ball to touch the ground? Use g = 10 m/s².

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long does it take before the bullet hits the ground?