Exam 3: Kinematics in Two Dimensions

A bicyclist is riding at a constant speed along a straight-line path.The rider throws a ball straight up to a height a few meters above her head.Ignoring air resistance, where will the ball land?

A car travels along a highway with a velocity of 24 m/s, west.The car exits the highway; and 4.0 s later, its instantaneous velocity is 16 m/s, 45° north of west.What is the magnitude of the average acceleration of the car during the four-second interval?

3-2 A spaceship is observed traveling in the positive x direction with a speed of 150 m/s when it begins accelerating at a constant rate.The spaceship is observed 25 s later traveling with an instantaneous velocity of 1500 m/s at an angle of 55° above the +x axis. -What was the magnitude of the displacement of the spaceship during the 25 seconds?

A football is kicked with a speed of 18 m/s at an angle of 65° to the horizontal. -How long is the football in the air? Neglect air resistance.

3-11 Two cars approach each other on a straight and level road.Car A is traveling at 75 km/h, due north and car B is traveling at 45 km/h, due south.Both velocities are measured relative to the ground. -What is the velocity of car A relative to an observer in car B?

What is the direction of the boat's average velocity for the one-hour trip?

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

3-12 A man at point A directs his rowboat due north toward point B, straight across a river of width 100 m.The river current is due east.The man starts across, rowing steadily at 0.75 m/s and reaches the other side of the river at point C, 150 m downstream from his starting point. -Two cars A and B approach each other at an intersection.Car A is traveling south at 20 m/s, while car B is traveling east at 17 m/s.What is the velocity of car A as described by the passengers in car B?

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

3-12 A man at point A directs his rowboat due north toward point B, straight across a river of width 100 m.The river current is due east.The man starts across, rowing steadily at 0.75 m/s and reaches the other side of the river at point C, 150 m downstream from his starting point. -What is the speed of the river?

An eagle is flying due east at 8.9 m/s carrying a gopher in its talons.The gopher manages to break free at a height of 12 m.What is the magnitude of the gopher's velocity as it reaches the ground? Note: effects of air resistance are not included in this calculation.

A football is kicked with a speed of 18 m/s at an angle of 65° to the horizontal. -What are the respective horizontal and vertical components of the initial velocity of the football?

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 rock is kicked horizontally at a speed of 15 m/s from the edge of a cliff.The rock strikes the ground 65 m from the foot of the cliff of height H as suggested in the figure, which is not drawn to scale.Neglect air resistance. -What is the approximate value of H, the height of the cliff?

A tennis ball is thrown vertically with an initial speed of 20.0 m/s at time t = 0 s.Approximately, what is the initial speed of the ball relative to an observer in a car that moves horizontally past the launch location with a constant speed of 30 m/s?

3-11 Two cars approach each other on a straight and level road.Car A is traveling at 75 km/h, due north and car B is traveling at 45 km/h, due south.Both velocities are measured relative to the ground. -A boat that can travel at 4.0 km/h in still water crosses a river with a current of 2.0 km/h.At what angle must the boat be pointed upstream (that is, relative to its actual path) to go straight across the river?

A train travels due south at 60 m/s.It reverses its direction and travels due north at 60 m/s. What is the change in velocity of the train?

3-11 Two cars approach each other on a straight and level road.Car A is traveling at 75 km/h, due north and car B is traveling at 45 km/h, due south.Both velocities are measured relative to the ground. -A ferry can travel at an optimal speed of 8 km/h in still water measured relative to the shore.What is the optimal speed of the ferry, relative to the shore, if it moves perpendicular to a 6 km/h current?

Airplane One flies due east at 250 km/h relative to the ground.At the same time, Airplane Two flies 325 km/h, 35° north of east relative to the ground.What is the velocity of Airplane One relative to Airplane Two?

3-10 During football practice, a football is kicked with a speed of 22 m/s at an angle of 60.0° relative to the positive x direction.At that instant, an observer rides past the football in a car that moves with a constant speed of 11 m/s in the positive x direction. -Complete the following statement: According to the observer in the car, the ball will