Question 1

Projectiles: A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground and experience negligible air resistance.
(a) How far from where the child is standing does the ball hit the ground?
(b) How long is the ball in flight before it hits the ground?

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Question 2

Relative velocity: A plane has an eastward heading at a speed of 156 m/s (relative to the air). A 20.0 m/s wind is blowing southward while the plane is flying. The velocity of the plane relative to the ground is

Accepted Answer

The velocity of the plane relative to the ground can be found using vector addition. The eastward velocity (156 m/s) and the southward wind velocity (20.0 m/s) form a right-angled triangle. The magnitude of the resultant velocity (relative to the ground) is $\sqrt{156^2 + 20^2} = 157$ m/s. The angle $\theta$ south of east is given by $\tan^{-1}(20/156) = 7.31^\circ$.

Question 3

Projectiles: A ball is thrown at a 60.0° angle above the horizontal across level ground. It is thrown from a height of 2.00 m above the ground with a speed of 20.0 m/s and experiences no appreciable air resistance. The time the ball remains in the air before striking the ground is closest to

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Question 4

Projectiles: What is the maximum distance we can shoot a dart, from ground level, provided our toy dart gun gives a maximum initial velocity of  and air resistance is negligible?

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Question 5

Relative velocity: A small boat is moving at a velocity of when it is accelerated by a river current perpendicular to the initial direction of motion. If the acceleration of the current is 0.750 m/s², what will be the new velocity of the boat after

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Question 6

Projectiles: A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground and experience negligible air resistance.
(a) What is the magnitude of the ball's velocity just before it hits the ground?
(b) At what angle below the horizontal does the ball approach the ground?

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Question 7

Projectiles: A projectile is fired from point 0 at the edge of a cliff, with initial velocity components of v₀_x = 60.0 m/s and v₀_y = 175 m/s, as shown in the figure. The projectile rises and then falls into the sea at point P. The time of flight of the projectile is 40.0 s, and it experiences no appreciable air resistance in flight. What is the magnitude of the velocity of the projectile 21.0 s after it is fired?

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Question 8

Projectiles: A catapult is tested by Roman legionnaires. They tabulate the results in a papyrus and 2000 years later the archaeological team reads (distances translated into modern units):  angle of  landing height = launch height. What is the initial velocity of launch of the boulders if air resistance is negligible?

Accepted Answer

Based on the information given in the problem, we know that the projectile lands at the same height it was launched from, which means the angle of launch must be 45 degrees. Using the kinematic equation:

d = vt*sin(2θ)/g

where d is the horizontal distance traveled, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity (9.81 m/s^2).

Substituting the given values and solving for v, we get:

v = d*g/(sin(2θ))

Plugging in the given distance and angle, we get:

v = (11 meters) * (9.81 m/s^2) / sin(90 degrees) ≈ 44 m/s

Therefore, the correct answer is A) 44 m/s.

Question 9

Relative velocity: A swimmer heading directly across a river 200 m wide reaches the opposite bank in 6 min 40 s, during which time she is swept downstream 480 m.
(a) How fast can she swim in still water?
(b) What is the speed of the current?

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Question 10

Projectiles: An airplane is flying at a speed of 2.00 × 10² m/s in level flight at an altitude of 8.00 × 10² m. A package is to be dropped from the airplane to land on a target on the ground. Ignore air resistance. (a) At what horizontal distance away from the target should the package be released so that it lands on the target? (b) In what direction relative to the horizontal will the package be traveling when it hits the ground?

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Question 11

Projectiles: A projectile is fired from point 0 at the edge of a cliff, with initial velocity components of v₀_x = 60.0 m/s and v₀_y = 175 m/s, as shown in the figure. The projectile rises and then falls into the sea at point P. The time of flight of the projectile is 40.0 s, and it experiences no appreciable air resistance in flight. What is the height of the cliff?

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Question 12

Projectiles: A rescue plane flying horizontally at  spots a survivor in the ocean  directly below and releases an emergency kit with a parachute. . Because of the shape of the parachute, it experiences insignificant horizontal air resistance. If the kit descends with a constant vertical acceleration of  how far away from the survivor will it hit the waves?

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Question 13

Projectiles: A plane flying at 70.0 m/s suddenly stalls. If the acceleration during the stall is 9.8 m/s² directly downward, the stall lasts 5.0 s, and the plane was originally climbing at 25° to the horizontal, what is the velocity after the stall?

Accepted Answer

The plane's initial velocity has a horizontal component of 70.0 m/s * cos 25° = 63.6 m/s and a vertical component of 70.0 m/s * sin 25° = 29.3 m/s. During the stall, the horizontal component of velocity remains constant, while the vertical component changes by -9.8 m/s^2 * 5.0 s = -49.0 m/s. Therefore, the velocity after the stall is 63.6 m/s at 17° below the horizontal.

Question 14

Projectiles: A rock is thrown at a window that is located 18.0 m above the ground. The rock is thrown at an angle of 40.0° above horizontal. The rock is thrown from a height of 2.00 m above the ground with a speed of 30.0 m/s and experiences no appreciable air resistance. If the rock strikes the window on its upward trajectory, from what horizontal distance from the window was it released?

Accepted Answer

The vertical motion equation is used to find the time it takes for the rock to reach the window's height. Then, using the horizontal motion equation, the horizontal distance is calculated.

Question 15

Relative velocity: A long-distance swimmer is able to swim through still water at 4.0 km/h. She wishes to try to swim from Port Angeles, Washington, directly north to Victoria, British Columbia, a distance of 50 km. An ocean current flows through the Strait of Juan de Fuca from west to east at 3.0 km/h. In what direction (relative to north) should she swim to make the crossing along a straight line between the two cities?

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Question 16

Projectiles: A hobby rocket reaches a height of  and lands  from the launch point with no air resistance. What was the angle of launch?

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Question 17

Projectiles: A hiker throws a stone from the upper edge of a vertical cliff. The stone's initial velocity is 25.0 m/s directed at 40.0° with the face of the cliff, as shown in the figure. The stone hits the ground 3.75 s after being thrown and feels no appreciable air resistance as it falls.
(a) What is the height of the cliff?
(b) How far from the foot of the cliff does the stone land?
(c) How fast is the stone moving just before it hits the ground?

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Question 18

Projectiles: A projectile returns to its original height 4.08 s after being launched, during which time it travels 76.2 m horizontally. If air resistance can be neglected, what was the projectile's initial speed?

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Question 19

Relative velocity: You want to swim straight across a river that is  wide. You find that you can do this if you swim at an angle of θ = 28° from the upstream direction at a constant rate of  relative to the water. At what rate does the river flow? The angle θ is measured from the river bank (directly upstream is  while directly across the river is

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Question 20

Relative velocity: An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of 120 m/s. If a constant wind blows at 10.0 m/s due west during the flight, what direction must the plane fly relative to north to arrive at the destination?

Accepted Answer

To arrive directly north at the destination despite the westward wind, the plane must compensate by flying slightly east of north. The angle θ can be found using trigonometry, where tan(θ) = wind speed / plane speed = 10 / 120. Solving for θ gives an angle slightly less than 5° east of north, which matches choice A, 4.78° east of north.

Quiz 4: Newtons Laws of Motion

Relative velocity: A plane has an eastward heading at a speed of 156 m/s (relative to the air) . A 20.0 m/s wind is blowing southward while the plane is flying. The velocity of the plane relative to the ground is

Projectiles: A ball is thrown at a 60.0° angle above the horizontal across level ground. It is thrown from a height of 2.00 m above the ground with a speed of 20.0 m/s and experiences no appreciable air resistance. The time the ball remains in the air before striking the ground is closest to

Projectiles: What is the maximum distance we can shoot a dart, from ground level, provided our toy dart gun gives a maximum initial velocity of and air resistance is negligible?

Relative velocity: A small boat is moving at a velocity of when it is accelerated by a river current perpendicular to the initial direction of motion. If the acceleration of the current is 0.750 m/s², what will be the new velocity of the boat after

Relative velocity: A swimmer heading directly across a river 200 m wide reaches the opposite bank in 6 min 40 s, during which time she is swept downstream 480 m. (a) How fast can she swim in still water? (b) What is the speed of the current?

Projectiles: A plane flying at 70.0 m/s suddenly stalls. If the acceleration during the stall is 9.8 m/s² directly downward, the stall lasts 5.0 s, and the plane was originally climbing at 25° to the horizontal, what is the velocity after the stall?

Projectiles: A hobby rocket reaches a height of and lands from the launch point with no air resistance. What was the angle of launch?

Projectiles: A projectile returns to its original height 4.08 s after being launched, during which time it travels 76.2 m horizontally. If air resistance can be neglected, what was the projectile's initial speed?

Quiz 4: Newtons Laws of Motion

Relative velocity: A plane has an eastward heading at a speed of 156 m/s (relative to the air) . A 20.0 m/s wind is blowing southward while the plane is flying. The velocity of the plane relative to the ground is

Projectiles: A ball is thrown at a 60.0° angle above the horizontal across level ground. It is thrown from a height of 2.00 m above the ground with a speed of 20.0 m/s and experiences no appreciable air resistance. The time the ball remains in the air before striking the ground is closest to

Projectiles: What is the maximum distance we can shoot a dart, from ground level, provided our toy dart gun gives a maximum initial velocity of and air resistance is negligible?

Relative velocity: A small boat is moving at a velocity of when it is accelerated by a river current perpendicular to the initial direction of motion. If the acceleration of the current is 0.750 m/s2, what will be the new velocity of the boat after

Relative velocity: A swimmer heading directly across a river 200 m wide reaches the opposite bank in 6 min 40 s, during which time she is swept downstream 480 m. (a) How fast can she swim in still water? (b) What is the speed of the current?

Projectiles: A plane flying at 70.0 m/s suddenly stalls. If the acceleration during the stall is 9.8 m/s2 directly downward, the stall lasts 5.0 s, and the plane was originally climbing at 25° to the horizontal, what is the velocity after the stall?

Projectiles: A hobby rocket reaches a height of and lands from the launch point with no air resistance. What was the angle of launch?

Projectiles: A projectile returns to its original height 4.08 s after being launched, during which time it travels 76.2 m horizontally. If air resistance can be neglected, what was the projectile's initial speed?

Relative velocity: A small boat is moving at a velocity of when it is accelerated by a river current perpendicular to the initial direction of motion. If the acceleration of the current is 0.750 m/s², what will be the new velocity of the boat after

Projectiles: A plane flying at 70.0 m/s suddenly stalls. If the acceleration during the stall is 9.8 m/s² directly downward, the stall lasts 5.0 s, and the plane was originally climbing at 25° to the horizontal, what is the velocity after the stall?