Question 1

3-4
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively.
-A quarterback throws a pass at an angle of 35° above the horizontal with an initial speed of 25 m/s.The ball is caught by the receiver 2.55 seconds later.Determine the distance the ball was thrown.
A)13 m
B)18 m
C)36 m
D)52 m
E)72 m

Accepted Answer

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

vx = vcosθ = 25cos35° ≈ 20.5 m/s
vy = vsinθ = 25sin35° ≈ 14.4 m/s

Then, we can use the vertical motion equation to find the time it takes for the ball to reach its highest point:

vy = voy - gt
0 = 14.4 - 9.8t
t = 1.47 s

Since the total time in the air is 2.55 s, the time the ball spends falling from its highest point to the receiver's hands is:

t_fall = 2.55 s - 1.47 s = 1.08 s

During this time, the ball will fall a distance equal to:

Δy = voyt_fall - (1/2)gt_fall^2
Δy = 14.4(1.08) - (1/2)(9.8)(1.08)^2
Δy ≈ 6.4 m

Therefore, the receiver must have been 6.4 m below the quarterback when he caught the ball. To find the total distance the ball traveled, we can use the horizontal component of the velocity:

d = vx*t_total
d = 20.5*2.55
d ≈ 52 m

So the answer is D, 52 m.

Question 2

3-5 A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. -What is the magnitude of the acceleration of the shell just before it strikes the ground? A)4.0 m/s² B)9.8 m/s² C)82 m/s² D)170 m/s² E)330 m/s²

Accepted Answer

Since the shell is fired horizontally, there is no initial vertical velocity. Therefore, the only force acting on the shell in the vertical direction is gravity (downward). Using the kinematic equation,
y = y0 + v0y t + 1/2 at^2
where y = -80 m (taking upwards as positive), y0 = 0, v0y= 0, and solving for t, we get t = 4 seconds. 
Now, using the horizontal motion of the shell, we can find the initial horizontal velocity (v0x).
x = v0x t
v0x = 332.5 m/s
Finally, using the kinematic equation,
x = x0 + v0x t + 1/2 at^2
where x = 1330 m, x0 = 0, v0x = 332.5 m/s, and t = 4 seconds, we can solve for a (the magnitude of acceleration).
a = 82.1875 m/s^2 ≈ 9.8 m/s^2
Therefore, the best choice is B.

Question 3

3-5
A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. 
-What is the magnitude of the velocity of the shell as it hits the ground?
A)4.0 m/s
B)9.8 m/s
C)82 m/s
D)170 m/s
E)330 m/s

Accepted Answer

The answer of 3-5
A shell is fired with a horizontal...

Question 4

A tennis ball is thrown upward at an angle from point A.It follows a parabolic trajectory and hits the ground at point D.At the instant shown, the ball is at point B.Point C represents the highest position of the ball above the ground. 
-While in flight, how do the x and y components of the velocity vector of the ball compare at the points B and C?
A)The velocity components are non-zero at B and zero at C.
B)The x components are the same; the y component at C is zero m/s.
C)The x components are the same; the y component has a larger magnitude at C than at B.
D)The x component is larger at C than at B; the y component at B points up while at C, it points downward.
E)The x component is larger at B than at C; the y component at B points down while at C, it points upward.

Accepted Answer

At point B, the ball is still moving upward and in the direction of the initial velocity, so the x and y components of the velocity vector are both non-zero. 
At point C, the ball has reached its maximum height and is momentarily at rest before it starts falling back down. Therefore, the y component of the velocity vector is zero. However, the x component remains the same because there is no force acting on the ball in the horizontal direction.

Question 5

3-4
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively.
-Determine the initial speed of the projectile.
A)40 m/s
B)50 m/s
C)60 m/s
D)70 m/s
E)80 m/s

Accepted Answer

The initial speed of the projectile can be found using the Pythagorean theorem:

initial speed = √(horizontal velocity² + vertical velocity²)
initial speed = √(30² + 40²)
initial speed = √(900 + 1600)
initial speed = √2500
initial speed = 50 m/s

Therefore, the correct answer is B.

Question 6

3-5
A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. 
-An arrow is shot horizontally from a height of 4.9 m above the ground.The initial speed of the arrow is 45 m/s.Neglecting friction, how long will it take the arrow to hit the ground?
A)9.2 s
B)6.0 s
C)1.0 s
D)1.4 s
E)4.6 s

Accepted Answer

The answer of 3-5
A shell is fired with a horizontal...

Question 7

3-5
A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. 
-A basketball is launched with an initial speed of 8.0 m/s and follows the trajectory shown.The ball enters the basket 0.96 s after it is launched.What are the distances x and y? Note: The drawing is not to scale.  x y
A)5.4 m 0.73 m
B)7.7 m 0.91 m
C)5.4 m 0.91 m
D)5.7 m 0.73 m
E)5.4 m 5.4 m

Accepted Answer

The answer of 3-5
A shell is fired with a horizontal...

Question 8

3-5
A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. 
-Determine the initial speed of the shell.
A)4.0 m/s
B)9.8 m/s
C)82 m/s
D)170 m/s
E)330 m/s

Accepted Answer

The answer of 3-5
A shell is fired with a horizontal...

Question 9

3-5
A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. 
-A cannonball at ground level is aimed 30.0° above the horizontal and is fired with an initial speed of 125 m/s.How far away from the cannon will the cannonball hit the ground?
A)125 m
B)138 m
C)695 m
D)1040 m
E)1380 m

Accepted Answer

The answer of 3-5
A shell is fired with a horizontal...

Question 10

3-4
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively.
-What is the magnitude of the projectile's velocity just before it strikes the ground?
A)zero m/s
B)9.8 m/s
C)30 m/s
D)40 m/s
E)50 m/s

Accepted Answer

We can use the Pythagorean theorem to find the magnitude of the velocity:
v = √(30^2 + 40^2) = 50 m/s

Question 11

A spring-loaded gun is aimed horizontally and is used to launch identical balls with different initial speeds.The gun is at a fixed position above the floor.The balls are fired one at a time.  If the speed of the second ball fired is twice the speed of the first ball fired, how is the horizontal range (denoted R in the figure) affected?
A)The range for both balls will be the same.
B)The range of the second ball will be half as much as that of the first ball.
C)The range of the second ball will be twice as large as that of the first ball.
D)The range of the second ball is about 1.4 times larger than that of the first ball.
E)The range of the second ball will be smaller than that of the first ball by a factor of 1.4.

Accepted Answer

The answer of A spring-loaded gun is aimed horizontally and...

Question 12

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -What is the acceleration of the projectile when it reaches its maximum height? A)zero m/s² B)9.8 m/s², downward C)4.9 m/s², downward D)less than 9.8 m/s²and non-zero. E)Its magnitude is 9.8 m/s²;and its direction is changing.

Accepted Answer

The answer of 3-4
A projectile fired from a gun has...

Question 13

3-4
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively.
-At what angle is the projectile fired (measured with respect to the horizontal)?
A)37°
B)40°
C)45°
D)53°
E)60°

Accepted Answer

The answer of 3-4
A projectile fired from a gun has...

Question 14

3-3
A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s.
-What is the magnitude of the horizontal component of the projectile's displacement at the end of 2 s?
A)30 m
B)40 m
C)10 m
D)20 m
E)50 m

Accepted Answer

The answer of 3-3
A projectile is fired at an angle...

Question 15

A puck slides across a smooth, level tabletop at height H at a constant speed v_o.It slides off the edge of the table and hits the floor a distance x away as shown in the figure. What is the relationship between the distances x and H? A) B) C) D) E)

Accepted Answer

The answer of A puck slides across a smooth, level...

Question 16

3-4
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively.
-What is the speed of the projectile when it is at the highest point in its trajectory?
A)0 m/s
B)20 m/s
C)30 m/s
D)40 m/s
E)50 m/s

Accepted Answer

At the highest point of the projectile's trajectory, the vertical component of velocity is zero. Therefore, the speed of the projectile at the highest point is equal to its initial horizontal component of velocity, which is 30 m/s.

Question 17

3-4
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively.
-A projectile is fired horizontally with an initial speed of 57 m/s.What are the horizontal and vertical components of its displacement 3.0 s after it is fired? horizontal vertical
A)44 m -29 m
B)170 m zero m
C)170 m -44 m
D)210 m -44 m
E)210 m zero m

Accepted Answer

The horizontal component of displacement is given by:

distance = speed x time = 57 m/s x 3.0 s = 170 m (since there is no acceleration in the horizontal direction)

The vertical component of displacement is given by:

distance = initial velocity x time + 0.5 x acceleration x time^2

where the initial velocity is zero (since the projectile is fired horizontally) and the acceleration is -9.8 m/s^2 (since the projectile is subject to gravity).

distance = 0 x 3.0 s + 0.5 x (-9.8 m/s^2) x (3.0 s)^2 = -44.1 m (the negative sign indicates the displacement is in the downward direction)

Therefore, the answer is C: 170 m horizontal displacement and -44 m vertical displacement.

Question 18

3-4
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively.
-Approximately how long does it take the projectile to reach the highest point in its trajectory?
A)1 s
B)2 s
C)4 s
D)8 s
E)16 s

Accepted Answer

The answer of 3-4
A projectile fired from a gun has...

Question 19

A bullet is aimed at a target on the wall a distance L away from the firing position.Because of gravity, the bullet strikes the wall a distance $\Delta$y below the mark as suggested in the figure. Note: The drawing is not to scale.  If the distance L was half as large and the bullet had the same initial velocity, how would $\Delta$y be affected?
A)($\Delta$y will double.)
B)($\Delta$y will be half as large.)
C)($\Delta$y will be four times larger.)
D)($\Delta$y will be one fourth as large.)
E)($\Delta$y is not possible to determine unless numerical values are given for the distances.)

Accepted Answer

The answer of A bullet is aimed at a target...

Question 20

3-3
A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s.
-How long does it take the projectile to reach the highest point in its trajectory?
A)1.5 s
B)2.4 s
C)4.0 s
D)6.2 s
E)9.8 s

Accepted Answer

Using the kinematic equation for vertical motion:

y = y0 + V0yt - 1/2gt^2

At the highest point of the trajectory, the vertical velocity is zero, so V0y = V0sin(55°) = 28.6 m/s

Also, the displacement in the y-direction at the highest point is:

y = 0 - 0 - 1/2(9.81 m/s^2)t^2 = -4.9t^2

Setting V0y = 0 and solving for t:

0 = 28.6 - 9.81t 
t = 2.92 s

Therefore, it takes the projectile 2.92 seconds to reach the highest point in its trajectory.

Quiz 3: Kinematics in Two Dimensions

3-5 A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. -What is the magnitude of the acceleration of the shell just before it strikes the ground?

3-5 A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. -What is the magnitude of the velocity of the shell as it hits the ground?

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -Determine the initial speed of the projectile.

3-5 A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. -Determine the initial speed of the shell.

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -What is the magnitude of the projectile's velocity just before it strikes the ground?

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -What is the acceleration of the projectile when it reaches its maximum height?

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -At what angle is the projectile fired (measured with respect to the horizontal) ?

3-3 A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s. -What is the magnitude of the horizontal component of the projectile's displacement at the end of 2 s?

A puck slides across a smooth, level tabletop at height H at a constant speed v_o.It slides off the edge of the table and hits the floor a distance x away as shown in the figure. What is the relationship between the distances x and H?

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -What is the speed of the projectile when it is at the highest point in its trajectory?

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -Approximately how long does it take the projectile to reach the highest point in its trajectory?

3-3 A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s. -How long does it take the projectile to reach the highest point in its trajectory?

Quiz 3: Kinematics in Two Dimensions

3-5 A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. -What is the magnitude of the acceleration of the shell just before it strikes the ground?

3-5 A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. -What is the magnitude of the velocity of the shell as it hits the ground?

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -Determine the initial speed of the projectile.

3-5 A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff.The shell strikes the ground 1330 m from the base of the cliff.The drawing is not to scale. -Determine the initial speed of the shell.

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -What is the magnitude of the projectile's velocity just before it strikes the ground?

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -What is the acceleration of the projectile when it reaches its maximum height?

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -At what angle is the projectile fired (measured with respect to the horizontal) ?

3-3 A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s. -What is the magnitude of the horizontal component of the projectile's displacement at the end of 2 s?

A puck slides across a smooth, level tabletop at height H at a constant speed vo.It slides off the edge of the table and hits the floor a distance x away as shown in the figure. What is the relationship between the distances x and H?

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -What is the speed of the projectile when it is at the highest point in its trajectory?

3-4 A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. -Approximately how long does it take the projectile to reach the highest point in its trajectory?

3-3 A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s. -How long does it take the projectile to reach the highest point in its trajectory?

A puck slides across a smooth, level tabletop at height H at a constant speed v_o.It slides off the edge of the table and hits the floor a distance x away as shown in the figure. What is the relationship between the distances x and H?