Ms. Stadler
Physics CP
Two-Dimensional Motion Problem Set
Directions: Show all your work on another sheet of paper. Use the correct number of significant figures and
units. Box your answers.
Vector Analysis
1) Solve the following triangles using SOHCAHTOA and Pythagoras (Solve all to two significant figures)
a)
b)
c)


25o
295
15
33
10
o


2) Solve the following right triangles using SOHCAHTOA and Pythagoras.
a)
b)
c)
25.0 o
35.0 km
a
10.0 mi
116 m
36.0o
b
3) Convert the following vectors to x and y components
a) 35 km [32o N of E]
65.0 o
b) 1.6 x 104 m/s [25o W of S]
4) Convert the following x and y components to vectors. Give the magnitude, direction, and sketch the vector.
a) x: 2.75 km
y: 13.4 km
b) x: -111.0 ft
y: -44.0 ft
5) Add the following vectors using the add components method
a) 56 m/s [25.0o N of E] + 31 m/s [10.0o S of W]
b) 1.2 x 103 m [35o W of N] + 8.8 x 103 m [72o W of S] + 1.3 x 104 m [27o S of W]
Vector Word Problems
6) An archaeologist climbs the Great Pyramid in Giza, Egypt. The pyramid’s height is 136 m and its width is
2.30  102 m. What is the magnitude and the direction of the displacement of the archaeologist after she has
climbed from the bottom of the pyramid to the top?
7) A hiker walks 27.0 km from her base camp at 35° south of east. The next day, she walks 41.0 km in a
direction 65° north of east and discovers a forest ranger’s tower. Find the magnitude and direction of her
resultant displacement.
Ms. Stadler
Physics CP
8) A motor boat traveling 4.0 m/s, East encounters a current traveling 3.0 m/s, North.
a) What is the resultant velocity of the motor boat?
b) If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to
shore?
c) What distance downstream does the boat reach the opposite shore?
9) A sailboat is heading 35o East of North at 7.2 knots. The ocean current is 25o South of East at 1.2 knots.
What speed and direction is the sailboat tracking? (Find the answer using the add components method)
10) A B747 is crossing the Pacific at 420 knots on a heading of 44o S of W. Air Traffic Control radar is tracking
the plane at 470 knots [49o S of W]. What is the wind speed and direction? (Hint: Subtract heading vector
from the tracking vector to get the wind vector)
11) If one of the components of one vector along the direction of another vector is zero, what can you conclude
about these two vectors?
12) A roller coaster travels 41.1 m at an angle of 40.0° above the horizontal. How far does it move horizontally
and vertically?
13) Three airline executives are discussing ideas for developing flights that are more energy efficient.
Executive A: Because the Earth rotates from west to east, we could operate “static flights”—a helicopter or
airship could begin by rising straight up from New York City and then descend straight down four hours
later when San Francisco arrives below.
Executive B: This approach could work for one-way flights, but the return trip would take 20 hours.
Executive C: That approach will never work. Think about it. When you throw a ball straight up in the air, it
comes straight back down to the same point.
Executive A: The ball returns to the same point because Earth’s motion is not significant during such a
short time.
State which of the executives is correct, and explain why.
Projectile Motion Word Problems
14) A rifle is fired horizontally from a platform 10.0 m above level ground. The muzzle velocity (the speed at
which the bullet emerges from the barrel of the gun) is 550 m/s. How far downrange will the bullet hit the
ground?
15) A zookeeper finds an escaped monkey hanging from a light pole. Aiming her tranquilizer gun at the
monkey, she kneels 10.0 m from the light pole, which is 5.00 m high. The tip of her gun is 1.00 m above the
ground. At the same moment that the monkey drops a banana, the zookeeper shoots. If the dart travels at
50.0 m/s, will the dart hit the monkey, the banana, or neither one?
16) A stone thrown horizontally from the top of a 24 m tower hits the ground at a point 18 m from the base of
the tower.
a) Find the speed at which the stone was thrown.
b) Find the speed of the stone just before it hits the ground.
Ms. Stadler
Physics CP
17) A rock is thrown from the top of a 20.0 m building at an angle of 53 degrees above the horizontal. If the
horizontal range of the throw is equal to the height of the building, with what speed was the rock thrown.
What is the velocity of the rock just before it strikes the ground?
18) A ball is thrown straight upward and returns to the thrower’s hand after 3.00 s in the air. A second ball is
thrown at an angle of 30.0° with the horizontal. At what speed must the second ball be thrown to reach the
same height as the one thrown vertically?
19) A human cannonball is shot out a cannon at 45.0° to the horizontal with an initial speed of 25.0 m/s. A net is
positioned at a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the
net be placed in order to catch the human cannonball?
Multiple Choice
11) Vector A has a magnitude of 30 units. Vector B is perpendicular to vector A and has a magnitude of 40
units. What would the magnitude of the resultant vector A + B be?
a. 10 units
b. 50 units
c. 70 units
d. zero
12) What term represents the magnitude of a velocity vector?
a. acceleration
b. momentum
c. speed
d. velocity
13) A golfer takes two putts to sink his ball in the hole once he is on the green. The first putt displaces the ball
6.00 m east, and the second putt displaces the ball 5.40 m south. What displacement would put the ball in
the hole in one putt?
a. 11.40 m southeast
b. 8.07 m at 48.0º south of east
c. 3.32 m at 42.0º south of east
d. 8.07 m at 42.0º south of east
Use the diagram below to answer questions 14-15.
14) What is the direction of the resultant vector A + B?
a. 15º above the x-axis
b. 75º above the x-axis
c. 15º below the x-axis
d. 75º below the x-axis
Ms. Stadler
Physics CP
15) What is the direction of the resultant vector A – B?
a. 15º above the x-axis
b. 75º above the x-axis
c. 15º below the x-axis
d. 75º below the x-axis
Use the passage below to answer questions 16–17.
A motorboat heads due east at 5.0 m/s across a river that flows toward the south at a speed of 5.0 m/s.
16) What is the resultant velocity relative to an observer on the shore?
a. 3.2 m/s to the southeast
b. 5.0 m/s to the southeast
c. 7.1 m/s to the southeast
d. 10.0 m/s to the southeast
17) If the river is 125 m wide, how long does the boat take to cross the river?
a. 39 s
b. 25 s
c. 17 s
d. 12 s
Use the passage to answer questions 18–21.
A girl riding a bicycle at 2.0 m/s throws a tennis ball horizontally forward at a speed of 1.0 m/s from a height of
1.5 m. At the same moment, a boy standing on the sidewalk drops a tennis ball straight down from a height of
1.5 m.
18) What is the initial speed of the girl’s ball relative to the boy?
a. 1.0 m/s
b. 2.0 m/s
c. 1.5 m/s
d. 3.0 m/s
19) If air resistance is disregarded, which ball will hit the ground first?
a. the boy’s ball
b. neither
c. the girl’s ball
d. cannot be determined
20) If air resistance is disregarded, which ball will have a greater speed (relative to the ground) when it hits the
ground?
a. the boy’s ball
b. neither
c. the girl’s ball
d. cannot be determined
Ms. Stadler
Physics CP
21) What is the speed of the girl’s ball when it hits the ground?
a. 1.0 m/s
b. 6.2 m/s
c. 3.0 m/s
d. 8.4 m/s
22) A bowling ball was dropped from the same height and at the same time that a softball was thrown
horizontally. Neglecting air resistance, which statement is true?
a. The bowling ball hit the ground first.
b. The softball hit the ground first.
c. The bowling ball and softball hit the ground at the same time.
d. The bowling ball fell faster than the softball.
23) The path of a kicked football is shown in the diagram above. The dashed line shows the path of the ball if
the air resistance is neglected. Point X is a point along the path. Which arrow points in the direction of the
acceleration?
a. I
b. II
c. III
d. IV
24) A baseball is thrown across a field. Neglecting air resistance, which best describes the horizontal
components of the ball’s velocity and acceleration while it is in the air?
a. Velocity is constant; acceleration is decreasing.
b. Velocity is constant; acceleration is constant.
c. Velocity is decreasing; acceleration is decreasing.
d. Velocity is increasing; acceleration is constant.
Ms. Stadler
Physics CP
25) A 0.15-kg object is projected vertically into the air with a velocity of 30. m/s. How high above the ground is
the object after 3.3 seconds?
a. 46 m
b. 53 m
c. 110 m
d. 150 m
26) Four arrows are shot horizontally from the top of a tower, as shown below. Which path represents the arrows
with the greatest horizontal velocity?
a.
b.
c.
d.
1
2
3
4
27) A ball is thrown horizontally. Which factor will increase the flight time of the ball?
a. increasing the vertical height from which the ball is thrown
b. increasing the horizontal velocity of the ball
c. decreasing the horizontal velocity of the ball
d. decreasing the vertical height from which the ball is thrown
28) A ball is thrown with a velocity of 17.6 m/s at an angle of 40.0° to the horizontal. What horizontal distance
measured along the ground does the ball travel before striking the ground?
a. 15.6 m
b. 20.3 m
c. 31.2 m
d. 40.6 m
29) A projectile was launched horizontally with a velocity of 468 m/s, 1.86 m above the ground. How long did it
take the projectile to hit the ground?
a. 0.308 s
b. 0.380 s
c. 0.616 s
d. 1.32 s
Ms. Stadler
30) In the figure below, the magnitude of the ball’s velocity is least at location
a. A
b. B
c. C
d. D
Physics CP