Question 1

A projectile is fired from point 0 at the edge of a cliff, with initial velocity components of v₀_x= 60 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?

Accepted Answer

The answer of A projectile is fired from point 0...

Question 2

A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point with no air resistance. What was the angle of launch?

Accepted Answer

The correct answer is A because the angle of launch can be calculated using the formula:θ = arctan(2 * h / d)where h is the height reached by the rocket and d is the horizontal distance traveled by the rocket. Plugging in the given values, we get:θ = arctan(2 * 72.3 m / 111 m) = 69.0°

Question 3

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° = 29.9 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 final velocity has a horizontal component of 63.6 m/s and a vertical component of -19.1 m/s. The magnitude of the final velocity is sqrt(63.6^2 + (-19.1)^2) = 66.0 m/s, and the angle below the horizontal is arctan(-19.1/63.6) = 17°.

Question 4

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?

Accepted Answer

The answer of An airplane is flying at a speed...

Question 5

You want to swim straight across a river that is 76 m 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 1.5 m/s relative to the water. At what rate does the river flow? The angle θ is measured from the river bank (directly upstream is θ = 0° while directly across the river is θ = 90°).

Accepted Answer

The river flows at a rate of 1.3 m/s. This is because the swimmer's velocity relative to the water is 1.5 m/s, and the angle at which the swimmer is swimming is 28°. The velocity of the river is therefore 1.5 m/s * sin(28°) = 1.3 m/s.

Question 6

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

Accepted Answer

The answer of A ball is thrown at a 60.0°...

Question 7

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?

Accepted Answer

The answer of A hiker throws a stone from the...

Question 8

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

The plane must fly at an angle of 4.78° east of north to arrive at the destination. This is because the wind will push the plane westward, so the plane must fly slightly eastward to compensate.

Question 9

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?

Accepted Answer

The answer of A long-distance swimmer is able to swim...

Question 10

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?

Accepted Answer

The answer of A child throws a ball with an...

Question 11

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?

Accepted Answer

The answer of A projectile returns to its original height...

Question 12

What is the maximum distance we can shoot a dart, from ground level, provided our toy dart gun gives a maximum initial velocity of 2.78 m/s and air resistance is negligible?

Accepted Answer

The answer of What is the maximum distance we can...

Question 13

A small boat is moving at a velocity of 3.35 m/s 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 33.5 s?

Accepted Answer

The new velocity in the direction of the current is given by v = at = 0.750 m/s² * 33.5 s = 25.125 m/s. The resultant velocity is found using the Pythagorean theorem: √(3.35² + 25.125²) ≈ 25.3 m/s. The angle θ is given by tan⁻¹(25.125/3.35) ≈ 82.4°.

Question 14

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?

Accepted Answer

The answer of A projectile is fired from point 0...

Question 15

A rescue plane flying horizontally at 72.6 m/s spots a survivor in the ocean 182 m 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 5.82 m/s², how far away from the survivor will it hit the waves?

Accepted Answer

The answer of A rescue plane flying horizontally at 72.6...

Question 16

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?

Accepted Answer

The answer of A swimmer heading directly across a river...

Question 17

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?

Accepted Answer

The answer of A child throws a ball with an...

Question 18

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 plane's velocity relative to the ground is the vector sum of its velocity relative to the air and the wind's velocity. Using the Pythagorean theorem, the resultant speed is √(156² + 20²) = 157 m/s. The angle south of east is calculated using tan⁻¹(20/156) = 7.31°.

Question 19

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 answer of A rock is thrown at a window...

Question 20

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): Range = 0.20 km; angle of launch = π/4; landing height = launch height. What is the initial velocity of launch of the boulders if air resistance is negligible?

Accepted Answer

The range R of a projectile launched at an angle θ with initial velocity v is given by R = (v^2 * sin(2θ)) / g. Given R = 0.20 km = 200 m, θ = π/4, and g = 9.8 m/s², solving for v gives v = sqrt(R * g / sin(2θ)) = sqrt(200 * 9.8 / sin(π/2)) = 44 m/s.

Quiz 3: Motion in Two or Three Dimensions

A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point with no air resistance. What was the angle of launch?

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?

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

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?

What is the maximum distance we can shoot a dart, from ground level, provided our toy dart gun gives a maximum initial velocity of 2.78 m/s and air resistance is negligible?

A small boat is moving at a velocity of 3.35 m/s 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 33.5 s?

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?

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

Quiz 3: Motion in Two or Three Dimensions

A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point with no air resistance. What was the angle of launch?

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?

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

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?

What is the maximum distance we can shoot a dart, from ground level, provided our toy dart gun gives a maximum initial velocity of 2.78 m/s and air resistance is negligible?

A small boat is moving at a velocity of 3.35 m/s 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 33.5 s?

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?

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

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?

A small boat is moving at a velocity of 3.35 m/s 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 33.5 s?