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].
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?
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.