Question 1

In a room where g = 9.81 m/s²,a hockey puck slides off the edge of a platform with an initial velocity of 28.0 m/s horizontally.The height of the platform above the ground is 2.00 m.What is the speed of the puck just before it hits the ground? Ignore air.

Accepted Answer

The horizontal velocity remains constant at 28.0 m/s. The vertical velocity can be found using v = sqrt(2gh) = sqrt(2*9.81*2) = 6.26 m/s. The resultant speed is sqrt((28.0)^2 + (6.26)^2) = 28.7 m/s.

Question 2

A cat leaps to try to catch a bird.If the cat's jump was at 60° off the ground and its initial velocity was $2.74 \mathrm {~m} / \mathrm { s }$ what is the highest point of its trajectory,neglecting effects of air?

Accepted Answer

The highest point of the trajectory, or the maximum height $h$, can be calculated using the formula $h = \frac{v^2 \sin^2(\theta)}{2g}$, where $v$ is the initial velocity, $\theta$ is the launch angle, and $g$ is the acceleration due to gravity (approximately $9.81 \mathrm{m/s^2}$). Plugging in the given values: $h = \frac{(2.74)^2 \sin^2(60)}{2 \times 9.81}$, we find that $h \approx 0.29 \mathrm{m}$.

Question 3

At target practice,a rifle bullet is fired at an angle of 30° below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high.How far from the base of the cliff does it strike the level ground below if air effects are negligible?

Accepted Answer

The answer of At target practice,a rifle bullet is fired...

Question 4

A batter hits a home run in which the ball travels 110 m horizontally with no appreciable effects of air.If the ball left the bat at 50° above the horizontal just above ground level,how fast was it hit?

Accepted Answer

The answer of A batter hits a home run in...

Question 5

You throw a rock horizontally off a cliff with a speed of 20 m/s.Assuming no effects of air,after 2.0 s,the magnitude of the velocity of the rock is closest to

Accepted Answer

The magnitude of the velocity of the rock can be found using the Pythagorean theorem, combining the horizontal velocity (which remains constant at 20 m/s due to no horizontal forces) and the vertical velocity (which increases due to gravity, $9.8 m/s^2$). After 2.0 s, the vertical velocity is $9.8 m/s^2 \times 2.0 s = 19.6 m/s$. The magnitude of the total velocity is $\sqrt{(20^2 + 19.6^2)} \approx 28 m/s$.

Question 6

A shell is launched with a velocity of 100 m/s at an angle of 30.0° above horizontal from a point on a cliff 50.0 m above a level plain below.How far from the base of the cliff does the shell strike the ground? There are no appreciable effects of air,and g = 9.80 m/s² at the location of the cliff.

Accepted Answer

The answer of A shell is launched with a velocity...

Question 7

A marble moving 1.48 m/s rolls off the top edge of a 125-cm high table in a room where there is no appreciable air resistance and the free-fall acceleration is 9.80 m/s².Neglect effects of air. (a)How far from the base of the table will it strike the floor? (b)How long will it be in the air?

Accepted Answer

The answer of A marble moving 1.48 m/s rolls off...

Question 8

A football kicker is attempting a field goal from $44 \mathrm {~m}$ out.The ball is kicked and just clears the lower bar with a time of flight of $2.9 \mathrm {~s}$ If the angle of the kick was 45°,what was the initial speed of the ball,assuming no effects of air?

Accepted Answer

The initial speed of the ball can be found using the range formula for projectile motion: $R = \frac{v^2 \sin 2\theta}{g}$, where $R$ is the range (44 m), $v$ is the initial speed, $\theta$ is the angle of projection (45°), and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Since $\sin(2 \times 45°) = \sin(90°) = 1$, the formula simplifies to $R = \frac{v^2}{g}$. Rearranging for $v$, we get $v = \sqrt{Rg}$. Substituting $R = 44 \, \text{m}$ and $g = 9.8 \, \text{m/s}^2$, we find $v = \sqrt{44 \times 9.8} \approx 21.5 \, \text{m/s}$.

Question 9

A hockey puck slides off the edge of a horizontal platform with an initial velocity of 20 m/s horizontally.The effects of air are negligible.The height of the platform 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?

Accepted Answer

Since the puck experiences a free fall motion after leaving the platform, we can use the kinematic equation:

vf^2 = vi^2 + 2gh

where vf is the final vertical velocity, vi is the initial vertical velocity (which is 0 m/s), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the platform (2.0 m).

Simplifying the equation, we get:

vf = sqrt(2gh)

vf = sqrt(2 x 9.8 m/s^2 x 2.0 m)

vf = 6.3 m/s (rounded to one decimal place)

Therefore, the magnitude of the vertical component of the velocity of the puck just before it hits the ground is 6.3 m/s. Option B is the correct answer.

Question 10

A hockey puck slides off the edge of a platform with an initial velocity of 20 m/s horizontally.The height of the platform above the ground is 2.0 m.What is the magnitude of the velocity of the puck just before it touches the ground? You can neglect air.

Accepted Answer

The magnitude of the velocity just before the puck touches the ground can be found using the Pythagorean theorem, combining the horizontal and vertical components of velocity. The horizontal velocity remains constant at 20 m/s because there is no horizontal acceleration. The vertical velocity can be found using the equation $v = \sqrt{2gh}$, where $g$ is the acceleration due to gravity (9.8 m/s$^2$) and $h$ is the height (2.0 m). This gives a vertical velocity of $\sqrt{2 \times 9.8 \times 2} = \sqrt{39.2} \approx 6.26$ m/s. The total velocity just before touching the ground is $\sqrt{20^2 + 6.26^2} \approx 20.78$ m/s, which rounds to 21 m/s.

Question 11

A fisherman casts his bait toward the river at an angle of 25° above the horizontal.As the line unravels,he notices that the bait and hook reach a maximum height of $2.9 \mathrm {~m}$ What was the initial velocity he launched the bait with? Assume that the line exerts no appreciable drag force on the bait and hook and that is the effects of air are negligible.

Accepted Answer

The correct answer is A because the initial velocity is 18 m/s.

Question 12

A ball rolls over the edge of a platform with a horizontal velocity of magnitude v.The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m.What is the magnitude of v if you can ignore air?

Accepted Answer

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

Question 13

A celebrating student throws a water balloon horizontally from a dormitory window that is 50 m above the ground.It hits the ground at a point 60 m from the building.Ignore air.
(a)What will be the horizontal component of the velocity of the balloon just before it hits the ground?
(b)What will be the magnitude of the vertical velocity of the balloon just before it hits the ground?

Accepted Answer

The answer of A celebrating student throws a water balloon...

Question 14

A hockey puck slides off the edge of a horizontal platform with an initial velocity of 28.0 m/shorizontally in a city where the free-fall acceleration is 9.81 m/s².The height of the platform 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 if you ignore the effects of air?

Accepted Answer

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

Question 15

A girl throws a rock horizontally with a speed of 12 m/s from a bridge.It falls 2.28 s before hitting the water below.Neglect air.
(a)How high is the bridge from the water below?
(b)How far horizontally does the rock travel before striking the water?

Accepted Answer

The answer of A girl throws a rock horizontally with...

Question 16

Enzo throws a rock horizontally with a speed of 12 m/s from a bridge.It falls for 2.28 s before reaching the water below.Ignore air.Just as the rock reaches the water,find
(a)the horizontal component of its velocity.
(b)the speed with which it is moving.

Accepted Answer

The answer of Enzo throws a rock horizontally with a...

Question 17

A hunter points a rifle horizontally and holds it 3.30 m above the ground.The bullet leaves the barrel at 325 m/s.Ignore air and assume that free-fall acceleration is 9.80 m/s². (a)How long does it take for the bullet to strike the ground? (b)How far horizontally does it travel?

Accepted Answer

The answer of A hunter points a rifle horizontally and...

Question 18

A plane flying horizontally at a speed of 50 m/s and at an elevation of 160 m drops a package,and 2.0 s later it drops a second package.How far apart will the two packages land on the ground if effects of air resistance are negligible?

Accepted Answer

The first package has a 2-second head start, meaning it will travel an additional $50 \, \text{m/s} \times 2 \, \text{s} = 100 \, \text{m}$ horizontally compared to the second package.

Question 19

A ball rolls over the edge of a platform with only a horizontal velocity.The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m.What is the horizontal velocity of the ball just before it touches the ground? Neglect air.

Accepted Answer

The horizontal velocity of the ball is constant throughout its flight. The vertical velocity of the ball is zero when it leaves the platform and increases as it falls. The horizontal range of the ball is equal to the horizontal velocity multiplied by the time of flight. The time of flight can be found using the vertical motion equation:$$y = vi*t + 1/2*a*t^2$$where y is the vertical displacement, vi is the initial vertical velocity, a is the acceleration due to gravity, and t is the time of flight.Substituting the given values into the equation, we get:$$-1.6 = 0 + 1/2*(-9.8)*t^2$$Solving for t, we get:$$t = 0.632 s$$The horizontal velocity of the ball is then:$$v = d/t = 20 m / 0.632 s = 31.6 m/s$$The closest answer choice is A) 35 m/s.

Question 20

A projectile is shot horizontally at 23.4 m/s from the roof of a building 55 m tall.
Effects of air are negligible.
(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: Applying Newtons Laws

In a room where g = 9.81 m/s2,a hockey puck slides off the edge of a platform with an initial velocity of 28.0 m/s horizontally.The height of the platform above the ground is 2.00 m.What is the speed of the puck just before it hits the ground? Ignore air.

A cat leaps to try to catch a bird.If the cat's jump was at 60° off the ground and its initial velocity was 2.74 m/s2.74 \mathrm {~m} / \mathrm { s }2.74 m/s what is the highest point of its trajectory,neglecting effects of air?

At target practice,a rifle bullet is fired at an angle of 30° below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high.How far from the base of the cliff does it strike the level ground below if air effects are negligible?

A batter hits a home run in which the ball travels 110 m horizontally with no appreciable effects of air.If the ball left the bat at 50° above the horizontal just above ground level,how fast was it hit?

You throw a rock horizontally off a cliff with a speed of 20 m/s.Assuming no effects of air,after 2.0 s,the magnitude of the velocity of the rock is closest to

A shell is launched with a velocity of 100 m/s at an angle of 30.0° above horizontal from a point on a cliff 50.0 m above a level plain below.How far from the base of the cliff does the shell strike the ground? There are no appreciable effects of air,and g = 9.80 m/s2 at the location of the cliff.

A marble moving 1.48 m/s rolls off the top edge of a 125-cm high table in a room where there is no appreciable air resistance and the free-fall acceleration is 9.80 m/s2.Neglect effects of air. (a)How far from the base of the table will it strike the floor? (b)How long will it be in the air?

A football kicker is attempting a field goal from 44 m44 \mathrm {~m}44 m out.The ball is kicked and just clears the lower bar with a time of flight of 2.9 s2.9 \mathrm {~s}2.9 s If the angle of the kick was 45°,what was the initial speed of the ball,assuming no effects of air?