Question 1

A boy kicks a football from ground level with an initial velocity of 20 m/s at an angle of 30° above the horizontal.What is the horizontal distance to the point where the football hits the ground if we neglect air resistance?

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Question 2

You throw a rock horizontally off a cliff with a speed of 20 m/s and no significant air resistance.After 
,the magnitude of the velocity of the rock is closest to

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Question 3

An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 35° above the horizontal.How long does the athlete stay in the air,assuming no significant air resistance?

Accepted Answer

The time of flight in projectile motion is given by the formula $T = \frac{2u\sin\theta}{g}$, where $u$ is the initial velocity, $\theta$ is the launch angle, and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Plugging in the given values: $T = \frac{2 \times 9.14 \times \sin(35^\circ)}{9.8}$, we find that the time of flight is approximately 1.1 seconds.

Question 4

A hockey puck slides off the edge of a horizontal platform with an initial velocity of 28.0 m/s horizontally in a city where the acceleration due to gravity is 9.81 m/s².The puck experiences no significant air resistance as it falls.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?

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Question 5

A child is trying to throw a ball over a fence.She gives the ball an initial speed of 8.0 m/s at an angle of 40° above the horizontal.The ball leaves her hand 1.0 m above the ground and the fence is 2.0 m high.The ball just clears the fence while still traveling upwards and experiences no significant air resistance.How far is the child from the fence?

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Question 6

A projectile is fired from ground level with a speed of 150 m/s at an angle 30° above the horizontal on an airless planet where g = 10.0 m/s².What is the horizontal component of its velocity after 4.0 s?

Accepted Answer

First, we can find the initial horizontal and vertical components of the velocity:

Vx = 150 cos(30°) = 129.9 m/s
Vy = 150 sin(30°) = 75 m/s

Since there is no air resistance, the horizontal component of the velocity remains constant throughout the motion. Therefore, after 4.0 s, the horizontal velocity is still 129.9 m/s.

Alternatively, we can use the formula for horizontal displacement:

x = Vx * t = 129.9 m/s * 4.0 s = 519.6 m

Therefore, the horizontal component of the velocity after 4.0 s is 129.9 m/s or approximately 130 m/s (Choice C).

Question 7

A hockey puck slides off the edge of a horizontal platform with an initial velocity of 20 m/s horizontally and experiences no significant air resistance.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

The vertical component of the velocity is given by:$$v_{yf}^2 = v_{yi}^2 + 2g\Delta y$$where:* $v_{yf}$ is the final vertical velocity* $v_{yi}$ is the initial vertical velocity* $g$ is the acceleration due to gravity* $\Delta y$ is the change in heightIn this case, $v_{yi} = 0$, $\Delta y = -2.0 \ m$, and $g = 9.8 \ m/s^2$. Plugging these values into the equation, we get:$$v_{yf}^2 = 0 + 2(9.8 \ m/s^2)(-2.0 \ m) = -39.2 \ m^2/s^2$$Taking the square root of both sides, we get:$$v_{yf} = -6.3 \ m/s$$The negative sign indicates that the puck is moving downward.

Question 8

A boy throws a ball with an initial velocity of 25 m/s at an angle of 30° above the horizontal.If air resistance is negligible,how high above the projection point is the ball after 2.0 s?

Accepted Answer

The vertical component of the initial velocity is 25 m/s * sin(30°) = 12.5 m/s. After 2.0 s, the ball has traveled 12.5 m/s * 2.0 s = 25 m upward. The ball is also subject to gravity, which causes it to fall 4.9 m/s^2 * (2.0 s)^2 / 2 = 9.8 m downward. Therefore, the ball is 25 m - 9.8 m = 15.2 m above the projection point after 2.0 s.

Question 9

A boy throws a rock with an initial velocity of At 30.0° above the horizontal.How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s²?

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Question 10

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? The air resistance is negligibly small.

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 11

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 air resistance is negligible?

Accepted Answer

The horizontal distance between the two packages is determined by the horizontal speed of the plane and the time interval between the drops. The plane travels 50 m/s * 2 s = 100 m horizontally in 2 seconds, so the packages will land 100 m apart.

Question 12

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 resistance.

Accepted Answer

The horizontal velocity of the ball is constant throughout its flight. The vertical velocity of the ball is zero at the start of its flight 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 equation:$$t = \sqrt{\frac{2h}{g}}$$where h is the height of the platform and g is the acceleration due to gravity.The horizontal velocity of the ball can then be found using the equation:$$v = \frac{d}{t}$$where d is the horizontal range of the ball.Plugging in the given values, we get:$$v = \frac{20 m}{\sqrt{\frac{2(1.6 m)}{9.8 m/s^2}}} = 35 m/s$$

Question 13

A football kicker is attempting a field goal from 
Out.The ball is kicked and just clears the lower bar with a time of flight of 
If the angle of the kick was 45°,what was the initial speed of the ball,assuming no air resistance?

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Question 14

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 resistance.

Accepted Answer

The magnitude of the velocity just before the puck touches the ground can be found using the Pythagorean theorem, combining the horizontal velocity (which remains constant at 20 m/s due to no horizontal forces acting on the puck) and the vertical velocity it gains while falling. 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). Calculating the vertical velocity gives $v = \sqrt{2 \times 9.8 \times 2} = \sqrt{39.2} \approx 6.26$ m/s. Then, the total velocity just before touching the ground is $\sqrt{20^2 + 6.26^2} \approx 21$ m/s.

Question 15

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 
What is the highest point of its trajectory,neglecting air resistance?

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Question 16

A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m,as shown in the figure.The width of the pylon is very narrow,and the length of each propeller blade is 12 m.A tip of the propeller breaks off just when the propeller is vertical.The fragment flies off horizontally,falls,and strikes the ground at point P with negligible air resistance.Just before the fragment broke off,the propeller was turning uniformly,taking 1.2 s for each rotation.How far is point P from the base of the pylon?

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Question 17

An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 55° with the vertical.What is the length of the athlete's jump if air resistance is of no significance?

Accepted Answer

The length of the athlete's jump can be calculated using the formula for the range of a projectile: $R = \frac{v^2 \sin 2\theta}{g}$, where $v$ is the initial velocity, $\theta$ is the angle of projection with the horizontal, and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Given that the angle provided is with the vertical, we first convert it to the angle with the horizontal: $90° - 55° = 35°$. Substituting the given values: $R = \frac{(9.14)^2 \sin(2 \times 35°)}{9.8}$, we find that the length of the jump is approximately 8.0 meters.

Question 18

A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level.The ball lands 100 m down range from the base of the building.What was the initial velocity of the ball? Neglect air resistance and use g = 9.81 m/s².

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Question 19

A high-speed dart is shot from ground level with a speed of 150 m/s at an angle 30° above the horizontal.What is the vertical component of its velocity after 4.0 s if air resistance is neglected?

Accepted Answer

The vertical component of velocity can be found using the formula v_y = v*sin(theta), where v is the initial velocity and theta is the angle above the horizontal. 
v_y = 150*sin(30) = 75 m/s (upward) 
After 4 seconds, the vertical velocity will decrease due to gravity: 
v_y = v_y0 - gt 
v_y = 75 - 9.8*4 = 36 m/s (upward) 
Therefore, the best choice is B.

Question 20

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 
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 air resistance is negligible.

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Quiz 4: Two-Dimensional Kinematics

A boy kicks a football from ground level with an initial velocity of 20 m/s at an angle of 30° above the horizontal.What is the horizontal distance to the point where the football hits the ground if we neglect air resistance?

You throw a rock horizontally off a cliff with a speed of 20 m/s and no significant air resistance.After ,the magnitude of the velocity of the rock is closest to

An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 35° above the horizontal.How long does the athlete stay in the air,assuming no significant air resistance?

A projectile is fired from ground level with a speed of 150 m/s at an angle 30° above the horizontal on an airless planet where g = 10.0 m/s2.What is the horizontal component of its velocity after 4.0 s?

A boy throws a ball with an initial velocity of 25 m/s at an angle of 30° above the horizontal.If air resistance is negligible,how high above the projection point is the ball after 2.0 s?

A boy throws a rock with an initial velocity of At 30.0° above the horizontal.How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s2?

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? The air resistance is negligibly small.