2D Relative Motion Practice Problems
For each of the problems draw a well labeled diagram as a part of your solution.
1. A fisherman is crossing a 45.0 m wide river in a motorboat. The motorboat can travel at 12 m/s in
still water. The water in the river flows at 6.0 m/s [East]. If the fisherman points his boat due North
toward a dock that is directly across the river from his location.
a. How long does it take the boat to cross the river?
b. How far down the river from the dock will the fisherman be when he reaches the North
shore?
c. What is the velocity of his boat relative to the shore?
2. If the fisherman in question 1 wants to travel due North across the river so that he reaches the dock.
a. What direction must he point his motorboat?
b. What will be the magnitude of his velocity relative to the shore?
c. How long will it take him to cross the river?
3. An airplane that can fly 180 km/h through still air is flying to a destination that is 5.00 x 102 km due
West of its position. If the plane must fly through a cross wind with a velocity of 25 km/h [North].
a. In what direction must the pilot point the plane to travel due west and arrive directly at the
destination?
b. What would be the plane’s velocity relative to the ground?
c. How long will it take the plane to arrive at the destination?
d. How much longer does this trip take than if there was no wind at all?
4. If the pilot in question 3 does not adjust for the cross wind, how far away the intended destination
and in what direction would the plane after it had travelled 500 km west?
5. A truck is travelling due south at 70 km/h toward and intersection. At the same time, a car is
travelling due east at 80 km/h toward the same intersection. What is the velocity of the car relative
to the truck?
6. A gambler on a riverboat drops a quarter while attempting to put it in a slot machine. The quarter
rolls at 1.5 m/s due east across the deck of the boat. An observer on the shore sees the riverboat
travelling at 16.0 m/s [South] along the river. If the observer was able to see the quarter as it rolled
across the deck, what velocity would he observe relative to the shore?
7. A World War II submarine is travelling through the North Atlantic at 16 km/h when it fires a torpedo.
The velocity of the torpedo relative to the submarine is 50 km/h (in the direction of the motion of
the submarine). At the time there is a cross current of 4.5 km/h [E].
a. In what direction must the submarine shoot in order to hit a ship that is 1.5 km [N] of its
position? (Ans: [N3.9°W])
b. How many seconds will it take the torpedo to reach the ship? [Ans: 82 s]
8. A plane with an airspeed of 65.0 m/s [N] is flying through a wind with a velocity of 8.00 m/s [N45°E].
What is the velocity of the plane relative to the ground? (Ans: 70.9 m/s [N4.58°E])
9. If the plane in question 8 wanted to reach a destination that was 40.0 km North of its starting
position. (Ans: 70.4 m/s [N4.99°W])
a. What direction should the pilot point the plane?
b. How long would it take the plane to reach its destination?