Question

A river flows due south with a speed of 1.7 m/s . A man steers a motorboat across the river; his velocity relative to the water is 3.8 m/s due east. The river is 840 m wide.

What is the magnitude of his velocity relative to the earth?

What is the direction of his velocity relative to the earth?

How much time is required to cross the river?

How far south of his starting point will he reach the opposite bank?

Answer 1

Given velocity of river is 1.7m/s due South and velocity of motorboat relative to river is 3.8 m/s due East

in vector notation, velocity of river=v_r = -1.7 j

in vector notation, velocity of boat relative to river=v_br=3.8 i

therefore, in vector notation,velocity of boat relative to Earth = 3.8i-1.7j m/s

Magnitude of velocity = sqrt(3.8²+1.7²)=4.16 m/s

direction of velocity relative to Earth = tan^-1(1.7/3.8)=24.1^o clockise from East direction

Time required to cross the river = 840/1.7=494.1 seconds