Physics Relative motion

Question

A ferryboat, whose speed in still water is 4.00m/s, must cross a river whose current is 3.00m/s. The river runs from west to east and is 128m wide. The boat is pointed north.

a) If the boat does not compensate for the flow of the river water and allows itself to be pushed off course, what would be the new velocity of the boat? State both the magnitude and the direction of the velocity of the boat relative to the riverbank.

b) In part (a), what is the velocity of the boat across the river? How long would it take the boat to travel across the river?

c) The boat now compensates for the river current so that it travels straight across the river to the north without being pushed off course.

Answer 1

a) If the boat captain holds a direction of due North during the entire trip then the velocity of the boat = Sqrt(3^2+4^2)= 5 m/s. The direction is arctan(3/4)=36.9 degrees East of North.

b) Since the boat holds direction of North the entire trip and the distance is 128m, the time is 128/4=32 sec

c) To compensate for the current, the captain steers a course West of North at an angle of arcsin(3/4) = 48.6degrees crossing the river in 128/4/cos(48.6)= 48.4 seconds