River flow velocity?

Question

A river flows due south with a speed of 1.6 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.7 m/s due east. The river is 650 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

You have a vector where for instance Vx is say x-component of the speed and direction of man's attempt to maintain a boat's heading and Vy is the speed and direction of river flow.

a) What is the magnitude of his velocity relative to the earth?
|V|=sqrt(Vx^2 + Vy^2)

b)What is the direction of his velocity relative to the earth?
this is a bit tricky since no point of reference is given so be can assume that the boat is being steered to the west and river flows to the north.

A=arctan(Vy / Vx)

c)
How much time is required to cross the river?
t=S/V on in this case
t=S/Vx

d) So we assumed that it flows north. Darn! So

D=Vy t = Vy (S/Vx)