Question

Can someone give me a step-by-step process on how to solve this? I know the answer I just need to know how to do it for a test:

A man wishes to row the shortest possible distance from north to south across a river which is flowing at 2 km/hr from the east. He can row at 3 km/hr.
(a) In which direction should he steer?
(b) Suppose that when the man is in the middle of the river, a wind of 6 km/hr from the southwest starts.

In which direction should he steer to move straight across the river?

Answer 1

To row straight across a river, steer in the opposite direction of the current. To counterbalance wind, steer in the opposite direction of its force.

Step-by-step explanation:

To solve this problem, we need to consider the velocity of the river and the velocity of the boat. Let's break it down into two parts:

(a)Since the river is flowing from east to west, the man should steer in the direction directly opposite to the flow of the river. In this case, he should steer towards the east.

(b) When the wind starts blowing from the southwest, it will affect the boat's lateral movement. To move straight across the river, the man should steer in a direction that counterbalances the wind's force. In this case, he should steer towards the northeast.

Answer 2

a) The shortest possible distance will be traveled if he moves straight from one side of the bank to the next, without any diagonal movement. Thus, he should steer southeast in order to counter the flow of the river from the east and also move towards his destination in a straight line.

b) The x-component of this wind can be calculated using:
Wx = 6cos(45)
Wx = 4.24 km/hr
This is greater than the opposing flow of the river from the east. Therefore, should row in a direction due south west to counter the wind's force as well as move towards his destination.