A river flows due south with a speed of 1.6m/s . A man steers a motorboat across

Question

A river flows due south with a speed of 1.6m/s . A man steers a motorboat across the river; his velocity relative to the water is 4.6m/s due east. The river is 670m wide.

A.

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

Express your answer using two significant figures.

B.

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

Express your answer using two significant figures.

C.

How much time is required to cross the river?

Express your answer using two significant figures.

D.

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

Express your answer using two significant figures.

Explanation / Answer

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) = 4.87 m/s

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) = 19.18o

c)
How much time is required to cross the river?
t=S/V on in this case
t=S/Vx = 145.65 sec

d) So we assumed that it flows north. So,

D=Vy t = Vy (S/Vx) = 233.04 m

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