A river flows due south with a speed of 1.70 m/s . A man steers a motorboat acro

Question

A river flows due south with a speed of 1.70 m/s . A man steers a motorboat across the river; his velocity relative to the water is 4.50 m/s . The river is 700 m wide.

Part A

In which direction should the motorboat head in order to reach a point on the opposite bank directly east from the starting point? (The boat's speed relative to the water remains 4.50 m/s .)

answer in degrees north of east

Part B

What is the velocity of the boat relative to the earth?

Part C

How much time is required to cross the river?

Explanation / Answer

PART A:
Vr,e (velocity of river with respect to earth) = -1.7 j m/s
Vb,r(velocity of boat wrt to river ) must be at an angle x due north from east
Vbr = 4.5 cos x + 4.5 sin x

Vb,e(velocity of boat with respect to earth) = Vb,r + Vr,e
= 4.5 cos x + 4.5 sin x j-1.7 j
To cross the river in straight path directly east, j component should be 0
4.5 sin x -1.7 = 0
sin x = 1.7/4.5
x=22.2 degree
Answer: 22.2 degree north from east

PART B:
Vb,e = 4.5 cos x + 4.5 sin y j-1.7 j
= 4.5 cos 22.2 i+ (4.5 sin 22.2 -1.7 )j
= 4.17 i +0j
Answer: 4.17m/s

PART C:
time = distance/speed
= 700/4.17
= 168 seconds

Answer: 168 seconds

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