posted by Lilah .
A motorboat heads due east at 8.5 m/s across a river that flows to the south at a speed of 2.5 m/s.
a. What is the velocity of the boat relative to a stationary observer on the shore?
B. If the river is 1360 m wide, how long does it take the boat to cross the river?
C. How far downstream will the boat have traveled when it reaches the other side?
The 8.5 m/s east motorboat velocity is actually with respect to the water. It may be pointed or headed east, but that is not the direction it goes. It drifts downstream with the water.
(a) The velocity with respect to shore is the vector sum of 8.5 m/s east and 2.5 m/s south. The path makes an angle of arctan 2.5/8.5 = 16.4 degrees away from the straight-across direction.
(b) 1360 m/8.5 m/s = 160 s
(c) 2.5 m/s * 160 s = 400 m