Relative Motion Problems
1) Ravi is standing at the side of the road. Sue is standing in a vehicle. Ravi measures the vehicle traveling
east on the road at a speed of 20.0 m/s. Sue measures a bird traveling west at a speed of 15 m/s. Find the
Velocity of the bird relative to Ravi.
(5 m/s [E])
2) Nikki is sitting on the island. Raj is driving by on the boat at 40.0m/s and traveling north as measured by
Nikki. Raj launches a firework north and measures it to be traveling at 20.0m/s. Find the Velocity as measured
by Nikki.
(60.0m/s [N])
3) Bailey is standing at the side of the road. Sue is standing in a vehicle. Bailey measures a bird flying west at a
speed of 10.0m/s. Sue measures a bird flying west at a speed of 15 m/s. Find the velocity of the vehicle as
measured by Bailey. (5m/s[E])
4) Once again Nikki is on the island and Raj is on the boat. The boat drives through a flock of geese and Raj measures the geese
to be flying North at 5.0 m/s. Nikki measures the same geese to be flying north at 25.0 m/s. How fast is the boat traveling?
(20.0m/s [N])
5) Javon is standing at the side of the road. Javon measures Sue traveling West at a speed of 50.0m/s. Javon measures Bailey
traveling west at a speed of 100.0m/s. Bailey measures a plane flying east at a speed of 350.0 m/s relative to herself. Find the
velocity of the plane relative to Javon as well as the velocity of the plane relative to Sue. (250.0m/s[E], 300.0m/s[E])
6) Nikki is on the island, Ayaan is swimming in the water, and Ray is driving the boat. Nikki measures
Ayaan to be swimming at 2.00m/s. Nikki also measures Ray to be driving at 20.0m/s. Both Ray and Ayaan
are traveling East. What is Ayaan’s velocity as measured by Ray? (18.0m/s[W])
7) Isaiah is standing at the side of the road. Sue is standing in a vehicle. Isaiah measures the vehicle to be
traveling East on the road at 20.0m/s. Sue measures a bird traveling North at a speed of 20.0m/s. Find the
velocity of the bird as measured by Isaiah. (28.3m/s[N45.0oE])
8) Nikki is sitting on the island and Ray is driving the boat. Nikki measures the boat to be traveling South at 40.0m/s. Karl jumps
off the west side of the boat at a speed of 12.0m/s as measured by Ray. What is Karl’s speed as measured by Nikki?
(41.8m/s[S16.7oW])
9) Isaiah is standing at the side of the road. Sue is standing in a bus. Isaiah measures the bus to be traveling North at a speed of
20.0m/s. Sue is holding a ball 5.00 meters above the floor of the bus. She then drops the ball, assume the only force on the ball is
gravity. What is the speed of the ball, just before it hits the floor, as measured by Sue? What is the speed of the ball just before it
hits the floor as measured by Isaiah? Hint: Draw the picture as a side view. (9.90m/s, 22.3m/s)
10) Nikki is on the island and Ray is on the boat. Nikki measures the boat to be traveling North at 20.0m/s.
Ray drops his yo-yo from his waist to his feet, a height of 1.00 meter. What is the speed of Ray’s yo-yo
just before it hits the floor as measured by Ray? What is the speed of Ray’s yo-yo just before it hits the
floor as measured by Nikki? (4.43m/s, 20.5m/s)
11) Bob is standing at the side of the road. Sue is standing in a bus. Bob measures the bus to be traveling
North at a speed of 30.0 m/s. Sue is holding a ball 10.0 meters above the floor of the bus. She then drops the ball (assume the
only force acting on the ball is the force of gravity). What is the speed of the ball 1.00 second after the ball is released as
measured by Sue? What is the speed of the ball 1 second after the ball is released as measured by Bob? (9.81m/s, 31.6m/s)
12) A helicopter travels with an air speed of 55 m/s. The helicopter heads in the direction [W35 oN]. What is velocity relative to
the ground if the wind velocity is
a)
21 m/s [E]
b)
21 m/s [N 22oW]?
(39.7m/s[N37.3oW], 73.5m/s[W44.0oN])
13) While you are vacationing in Hawaii, you spot a plane traveling in the direction [60.0º S of E]. If its ground
velocity is 210.0 km/h and the wind speed is 150.0 km/h [south], what is the plane’s velocity relative to the air? Draw
a diagram. (110km/h[E16.9oS])