NAME
_______________ DATE ________________ CLASS __________________
Two-Dimensional Motion and Vectors
Mixed Review
1. The diagram indicates three positions to which a woman travels. She
starts at position A, travels 3.0 km to the west to point B, then 6.0 km
to the north to point C. She then backtracks, and travels 2.0 km to the
south to point D.
a. In the space provided, diagram the displacement vectors for each
segment of the woman’s trip.
b. What is the total displacement of the woman from her initial
position,
A, to her final position, D?
c. What is the total distance traveled by the woman from her initial
position, A, to her final position, D?
2. Two projectiles are launched from the ground, and both reach the same vertical height. However, projectile B
travels twice the horizontal distance as projectile A before hitting the ground.
a. How large is the vertical component of the initial velocity of projectile B compared with the vertical component
of the initial velocity of projectile A?
b. How large is the horizontal component of the initial velocity of projectile B compared with the horizontal
component of the initial velocity of projectile A?
c. Suppose projectile A is launched at an angle of 45 to the horizontal. What is the ratio, vB/vA, of the speed of
projectile B, vB, compared with the speed of projectile A, vA?
3. A passenger at an airport steps onto a moving sidewalk that is 100.0 m long and is moving at a speed of 1.5 m/s.
The passenger then starts walking at a speed of 1.0 m/s in the same direction as the sidewalk is moving. What is
the passenger’s velocity relative to the following observers?
a. A person standing stationary alongside to the moving sidewalk.
b. A person standing stationary on the moving sidewalk.
c. A person walking alongside the sidewalk with a speed of 2.0 m/s and in a direction opposite the motion of the
sidewalk.
d. A person riding in a cart alongside the sidewalk with a speed of 5.0 m/s and in the same direction in which the
sidewalk is moving.
e. A person riding in a cart with a speed of 4.0 m/s and in a direction perpendicular to the direction in which the
sidewalk is moving.
4. Use the information given in item 3 to answer the following questions:
a. How long does it take for the passenger walking on the sidewalk to get from one end of the sidewalk to the
other end?
b. How much time does the passenger save by taking the moving sidewalk instead of walking alongside it?
Original content Copyright © by Holt, Rinehart and Winston. Additions and changes to the original content are the responsibility of the instructor.
Holt Physics
17
Study Guide
FINDING RESULTANT VECTOR’S MAGNITUDE AND DIRECTIONS
5. In 1926, Gertrude Ederle of the United States became the first woman to swim across the English channel.
Suppose Ederle swam 25.2 km east from the coast near Dover, England, then made a 90 turn and traveled south
for 21.3 km to a point east of Calais, France. What was Ederle’s resultant displacement?
RESOLVING VECTORS
6. The landing speed of the space shuttle Columbia is 347 km/h. If the shuttle is landing at an angle of 15.0 with
respect to the horizontal, what are the horizontal and the vertical components of its velocity?
ADDING VECTORS ALGEBRAICALLY
7. In 1976, the Lockheed SR-71A Blackbird set the record speed for any airplane: 3.53  103 km/h. Suppose you
observe this plane ascending at this speed. For 20.0 s, it flies at an angle of 15.0 above the horizontal, then for
another 10.0 s its angle of ascent is increased to 35.0. Calculate the plane’s total gain in altitude, its total
horizontal displacement, and its resultant displacement.
PROJECTILES LAUNCHED HORIZONTALLY
8. Recall Elmer Trett, who in 1994 reached a speed of 372 km/h on his motorcycle. Suppose Trett drives off a
horizontal ramp at this speed and lands a horizontal distance of 40.0 m away from the edge of the ramp. What is
the height of the ramp? Neglect air resistance.
PROJECTILES LAUNCHED @ AN ANGLE
9. A scared kangaroo once cleared a fence by jumping with a speed of 8.42 m/s at an angle of 55.2 with respect to
the ground. If the jump lasted 1.40 s, how high was the fence? What was the kangaroo’s horizontal displacement?
RELATIVE MOTION
10. Turtles are fairly slow on the ground, but they are very good swimmers, as indicated by the reported speed of 9.0
m/s for the leatherback turtle. Suppose a leatherback turtle swims across a river at 9.0 m/s relative to the water. If
the current in the river is 3.0 m/s and it moves at a right angle to the turtle’s motion, what is the turtle’s
displacement with respect to the river’s bank after 1.0 min?
1. a. The diagram should indicate the relative distances
and directions for each segment of the path.
b. 5.0 km, slightly north of northwest
c. 11.0 km
2. a. The same
b. Twice as large
c. 1.58
3. a. 2.5 m/s, in the direction of the sidewalk’s motion
b. 1.0 m/s, in the direction of the sidewalk’s motion
c. 4.5 m/s, in the direction of the sidewalk’s motion
d. 2.5 m/s, in the direction opposite to the sidewalk’s
motion
e. 4.7 m/s, q = 32Åã
4. a. 4.0 Å~ 101 seconds
b. 6.0 Å~ 101 seconds
5. 33.00 km @ 42.6 S. of E.
6. Vx=335 km/h
Vy=89.8 km/h
7. ytot= 1.07 x 104 m
xtot= 2.69 x 104 m
d=2.89 x 104 m @ 21.7 above the horizontal
8. The ramp is .735 m above the ground
9. The fence is 2.44 m high
x = 6.73 m
10. x = 570 m @ 18 E. of N.