Deck 4: Kinematics in Two Dimensions

Question 1

Shown below are the velocity and acceleration vectors for a person in several different types of motion. In which case is the person slowing down and turning to his right?

A)
B)
C)
D)
E)

Answer 1

Question 2

Alice and Tom dive from an overhang into the lake below. Tom simply drops straight down from the edge, but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. Neither person experiences any significant air resistance. Compare the time it takes each of them to reach the lake below.

A) Alice reaches the surface of the lake first.
B) Tom reaches the surface of the lake first.
C) Alice and Tom will reach the surface of the lake at the same time.

Answer 2

Alice and Tom will reach the surface of the lake at the same time.

Question 3

Jan and Len throw identical rocks off a tall building at the same time. The ground near the building is flat. Jan throws her rock straight downward. Len throws his rock downward and outward such that the angle between the initial velocity of the rock and the horizon is 30°. Len throws the rock with a speed twice that of Jan's rock. If air resistance is negligible, which rock hits the ground first?

A) They hit at the same time.
B) Jan's rock hits first.
C) Len's rock hits first.
D) It is impossible to know from the information given.

Answer 3

They hit at the same time.

Question 4

A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will

A) be behind the package.
B) be over the package.
C) be in front of the package.
D) depend of the speed of the plane when the package was released.

Question 5

Object A has a position as a function of time given by _A(t) = (3.00 m/s)t + (1.00 m/s²)t² . Object B has a position as a function of time given by _B(t) = (4.00 m/s)t + (-1.00 m/s²)t²
. All quantities are SI units. What is the distance between object A and object B at time

A) 34.6 m
B) 15.0 m
C) 18.3 m
D) 3.46 m
E) 29.8 m

Question 6

Alice and Tom dive from an overhang into the lake below. Tom simply drops straight down from the edge, but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. Neither person experiences any significant air resistance. Just as they reach the lake below

A) the speed of Alice is larger than that of Tom.
B) the splashdown speed of Alice is larger than that of Tom.
C) they will both have the same speed.
D) the speed of Tom will always be 9.8 m/s larger than that of Alice.
E) the speed of Alice will always be 25 m/s larger than that of Tom.

Question 7

An object has a position given by = [2.0 m + (5.00 m/s)t] + [3.0 m - (2.00 m/s²)t²] , where quantities are in SI units. What is the speed of the object at time

A) 6.40 m/s
B) 9.43 m/s
C) 7.00 m/s
D) 7.65 m/s
E) 13.0 m/s

Question 8

A boy throws a rock with an initial velocity of at 30.0° above the horizontal. If air resistance is negligible, how long does it take for the rock to reach the maximum height of its trajectory?

A) 0.110 s
B) 0.194 s
C) 0.215 s
D) 0.303 s

Question 9

If you set the cruise control of your car to a certain speed and take a turn, the speed of the car will remain the same. Is the car accelerating?

A) Yes
B) No

Question 10

A monkey is sitting at the top of a tree 20 m above ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the person knows that the monkey is going to drop from the tree at the same instant that the person launches the food, how should the person aim the arrow containing the food? Air resistance is small enough to be ignored.

A) He should aim it at the monkey.
B) He should aim it below the monkey.
C) He should aim it above the monkey.

Question 11

A hockey puck slides off the edge of a table at point A with an initial velocity of 20.0 m/s and experiences no air resistance. The height of the tabletop above the ground is 2.00 m.
(a) What is the speed (not the velocity) of the puck just before it touches the ground?
(b) What is the distance between point A and the point where the puck hits the ground?

Question 12

An electron moves with a constant horizontal velocity of and no initial vertical velocity as it enters a deflector inside a TV tube. The electron strikes the screen after traveling horizontally and vertically upward with no horizontal acceleration. What is the constant vertical acceleration provided by the deflector? (The effects of gravity can be ignored.)

A) 2.5 × 10¹⁴ m/s²
B) 8.3 × 10² m/s²
C) 1.4 × 10⁴ m/s²
D) 1.2 × 10¹⁴ m/s²

Question 13

A hockey puck slides off the edge of a table with an initial velocity of 28.0 m/s. and experiences no air resistance. The height of the tabletop 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?

A) 77.2°
B) 72.6°
C) 12.8°
D) 12.6°
E) 31.8°

Question 14

The horizontal coordinates of a in a strong wind are given by where x and y are in meters, and t is in seconds.
(a) What is the acceleration of the Frisbee? Give a magnitude and a direction, measuring angles from the positive x direction.
(b) What is the magnitude of the velocity at accurate to the nearest

Question 15

If an object travels at a constant speed in a circular path, the acceleration of the object is

A) larger in magnitude the smaller the radius of the circle.
B) in the same direction as the velocity of the object.
C) smaller in magnitude the smaller the radius of the circle.
D) in the opposite direction of the velocity of the object.
E) zero.

Question 16

Point P in the figure indicates the position of an object traveling at constant speed clockwise around the circle. Which arrow best represents the direction of the acceleration of the object at point P?

A)
B)
C)
D)
E)

Question 17

While an object is in projectile motion (with upward being positive) with no air resistance

A) the horizontal component of its velocity remains constant and the horizontal component of its acceleration is equal to -g.
B) the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to -g.
C) the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to zero.
D) the vertical component of both its velocity and its acceleration remain constant.
E) the vertical component of its velocity remains constant and the vertical component of its acceleration is equal to -g.

Question 18

For general projectile motion, when the projectile is at the highest point of its trajectory

A) its acceleration is zero.
B) its velocity is perpendicular to the acceleration.
C) its velocity and acceleration are both zero.
D) the horizontal component of its velocity is zero.
E) the horizontal and vertical components of its velocity are zero.

Question 19

An object has a position given by = [2.0 m + (3.00 m/s)t] + [3.0 m - (2.00 m/s²)t²] , where all quantities are in SI units. What is the magnitude of the acceleration of the object at time t = 2.00 s?

A) 1.00 m/s²
B) 0.00 m/s²
C) 0.522 m/s²
D) 4.00 m/s²
E) 2.00 m/s²

Question 20

For an object in uniform circular motion, its velocity and acceleration vectors are always perpendicular to each other at every point in the path.

A) True
B) False

Question 21

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?

A) 574 m
B) 4.54 km
C) 406 m
D) 602 m

Question 22

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) 157 m/s at an angle 7.31° south of east.
B) 157 m/s at an angle 7.31° east of south.
C) 155 m/s at an angle 7.36° south of east.
D) 155 m/s at an angle 7.36° east of south.
E) 157 m/s at an angle 7.36° south of east.

Question 23

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?

Question 24

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?

Question 25

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?

A) 0.789 m
B) 1.58 m
C) 1.39 m
D) 0.394 m

Question 26

A swimmer heading directly across a river 200 m wide reaches the opposite bank in 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?

Question 27

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

A) 25.3 m/s at 82.4° from initial direction of motion
B) 25.3 m/s at 7.59° from initial direction of motion
C) 640.1 m/s at 82.4° from initial direction of motion
D) 640.1 m/s at 7.59° from initial direction of motion

Question 28

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

A) 69.0°
B) 67.4°
C) 22.6°
D) 44.8°

Question 29

A projectile is fired from point 0 at the edge of a cliff, with initial velocity components of v_0x = 60.0 m/s and v_0y = 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?

Question 30

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?

Question 31

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

A) 1.3 m/s
B) 0.70 m/s
C) 1.6 m/s
D) 1.8 m/s

Question 32

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) 16.2 s.
B) 3.07 s.
C) 3.32 s.
D) 3.53 s.
E) 3.64 s.

Question 33

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?

A) 4.78° east of north
B) 4.76° east of north
C) 85.2° west of north
D) 4.78° west of north
E) 4.76° west of north

Question 34

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?

Question 35

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?

A) 53.2 m
B) 48.7 m
C) 71.6 m
D) 29.8 m
E) 27.3 m

Question 36

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?

Question 37

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) 66 m/s at 17° below the horizontal
B) 66 m/s at 17° above the horizontal
C) 80 m/s at 37° below the horizontal
D) 80 m/s at 37° above the horizontal

Question 38

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

Question 39

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?

A) 44 m/s
B) 1.4 m/s
C) 22 m/s
D) 0.69 m/s

Question 40

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?

A) 37° west of north
B) 37° east of north
C) 41° west of north
D) 41° east of north
E) 49° west of north

Question 41

A plane flies directly between two cities, A and B, which are separated by 2300 mi. From A to B, the plane flies into a 65 mi/h headwind. On the return trip from B to A, the wind velocity is unchanged. The trip from B to A takes less than the trip from A to B. What is the airspeed of the plane, assuming it is the same in both directions?

A) 530 mi/h
B) 400 mi/h
C) 480 mi/h
D) 610 mi/h

Question 42

An object moves in a circle of radius R at constant speed with a period T. If you want to change only the period in order to cut the object's acceleration in half, the new period should be

A) T/4.
B) T/2.
C) T/ .
D) T .
E) 4T.

Question 43

A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 2.00 m making 7.00 revolutions every 10.0 seconds. What is the magnitude of the acceleration of the ball?

A) 67.9 m/s²
B) 38.7 m/s²
C) 29.3 m/s²
D) 14.8 m/s²
E) 74.2 m/s²

Question 44

A disk-shaped space station 175 m in diameter spins uniformly about an axis perpendicular to the plane of the disk through its center. How many rpm (rev/min) must this disk make so that the acceleration of all points on its rim is g/2?

Question 45

A satellite orbits the earth a distance of 1.50 × 10⁷ m above the planet's surface and takes 8.65 hours for each revolution about the earth. The earth's radius is 6.38 × 10⁶ m. The acceleration of this satellite is closest to

A) 0.0690 m/s².
B) 0.870 m/s².
C) 1.91 m/s².
D) 2.72 m/s².
E) 9.80 m/s².

Question 46

A cart is moving with a constant horizontal velocity of 5.00 m/s. A small pebble is launched from the front of the cart with a velocity of 8.00 m/s at 60.0° above the horizontal as measured relative to the cart (see figure) and experiences no significant air resistance. Just as the pebble returns to the level from which it was launched, its distance from the front of the cart is closest to

A) 2.83 m.
B) 4.60 m.
C) 5.66 m.
D) 9.19 m.
E) 11.3 m.

Question 47

A wind farm generator uses a two-bladed propeller (see figure) mounted on a pylon at a height of 20 m. The length of each propeller blade is 12 m. A small piece from the tip of the propeller breaks off when the propeller is vertical. At that instant, the period of the motion of the propeller is 1.2 s. The fragment flies off horizontally, falls with negligible air resistance, and strikes the ground at P.
(a) How far is point P from the base of the pylon?
(b) At what angle with respect to the vertical is the fragment moving just as it strikes the ground at P?

Question 48

An electrical motor spins at a constant If the armature radius is what is the acceleration of the outer edge of the armature?

A) 2403 m/s²
B) 844.4 m/s²
C) 241,100 m/s²
D) 84.40 m/s²

Question 49

Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 8.5 times that of particle B. The period of particle B is 2.0 times the period of particle A. The ratio of the radius of the motion of particle A to that of particle B is closest to

A) r_A/r_B = 2.1.
B) r_A/r_B = 4.3.
C) r_A/r_B = 18.
D) r_A/r_B = 0.24.
E) r_A/r_B = 17.

Question 50

An aircraft performs a maneuver called an "aileron roll." During this maneuver, the plane turns like a screw as it maintains a straight flight path, which sets the wings in circular motion. If it takes it 35 s to complete the circle and the wingspan of the plane is 11 m, what is the acceleration of the wing tip?

A) 0.18 m/s²
B) 0.99 m/s²
C) 5.6 m/s²
D) 1.0 m/s²