The law of addition of speeds. A swimmer swims across a river 100 m wide at a speed of 0.5 M / s relative to the water.

The law of addition of speeds. A swimmer swims across a river 100 m wide at a speed of 0.5 M / s relative to the water. If the swimmer’s speed is directed at an angle of 30 to the current, then he will reach the opposite bank in a time equal to?

Given:
v = 0.5 meters per second – the swimmer’s speed relative to the water;
a = 30 degrees – the angle between the direction of the swimmer’s speed and the current;
L = 100 meters – width of the river.
It is required to determine t (seconds) – the time it takes for the swimmer to reach the opposite bank of the river.
Let’s decompose the swimmer’s speed into two components: perpendicular to the bank v * cos (a) and parallel to the bank v * sin (a). The first component of the speed (perpendicular) is responsible for the time through which the swimmer swims across the river, and the second for the segment at which he deviates from the initial point. Then:
t = L / (v * cos (a) = 100 / (0.5 * cos (30)) = 100 / (0.5 * 0.87) = 100 / 0.435 = 230 seconds.
Answer: The swimmer will swim across the river in 230 seconds (3.8 minutes).