A swimmer jumps into a 5.1km wide river and swims straight for the other side at 0.87 km/h [N]. There is a current in the river 2.0 km/h [W].

Question

a) How long does it take the swimmer to reach the other side?
b) How far downstream has the current moved her before she reaches the other side?

Answer 1

To solve this problem, we can use the concept of vector addition.

a) To find how long it takes the swimmer to reach the other side, we can use the formula:

Time = Distance / Speed

In this case, the distance is the width of the river, 5.1 km, and the speed is the swimmer's speed relative to the water, which is 0.87 km/h. Therefore, the time taken by the swimmer to reach the other side is:

Time = 5.1 km / 0.87 km/h = 5.86 hours

b) To find how far downstream the current moves her before she reaches the other side, we can use the formula:

Distance = Speed × Time

The speed of the current is 2.0 km/h. The time taken to reach the other side is 5.86 hours. Therefore, the distance downstream the current moves her is:

Distance = 2.0 km/h × 5.86 hours = 11.72 km

So, the swimmer is moved 11.72 km downstream by the current before reaching the other side.