Question

A 200m wide river has a uniform flow speed of 1.1 m/s through a jungle and towards the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 4 m/s with respect to the river. There is a clearing on the north bank 82 m upstream from a point directly opposite to the south bank.

(a) in what direction must the boat be pointed in order to travel in a straight line and land on the clearing on the north bank?
(b) How long will the boat take to cross the river and land in the clearing?

Answer 1

The boat must be pointed slightly to the west of directly north in order to travel in a straight line and land on the clearing on the north bank. The time it will take for the boat to cross the river and land in the clearing can be calculated using basic trigonometry.

Step-by-step explanation:

To determine the direction the boat must be pointed in order to travel in a straight line and land on the clearing on the north bank, we need to consider the velocity of the river and the velocity of the boat. Since the boat has a constant speed of 4 m/s with respect to the river, it needs to aim slightly upstream in order to counteract the downstream motion of the river. Therefore, the boat must be pointed slightly to the west of directly north.

To find the time it will take for the boat to cross the river and land in the clearing, we can use the concept of relative velocities. The boat needs to travel a distance of 200 m (width of the river) in a direction slightly to the west of directly north at a speed of 4 m/s with respect to the river. Using basic trigonometry, we can calculate the time it will take for the boat to cross the river and land in the clearing.