The stream of a river is flowing with velocity 1 km/h.What should be the direction of a swimmer to cross the river straight if he can swim at the rate of 2 km/h in still water.
draw the figure. downsteam, 1, on the hypotenuse upstream 2
the angle upstream measured from the normal across the stream is arcsin 1/2 or 30 deg
To determine the direction a swimmer needs to take to cross a river straight, we need to consider the velocity of the stream and the swimmer's swimming speed.
The stream's velocity is given as 1 km/h, and the swimmer can swim at a rate of 2 km/h in still water. To cross the river straight, the swimmer needs to compensate for the stream's velocity, effectively canceling out its effect.
To achieve this, the swimmer needs to swim in a direction that is a combination of the stream's direction and some component in the opposite direction to counteract the stream's motion.
We can use vector addition to find this resultant direction. The swimmer's swimming speed (2 km/h) can be considered as the magnitude of the swimmer's velocity vector. The stream's velocity (1 km/h) can be considered as the magnitude of the stream's velocity vector.
To add the vectors, we subtract the stream's velocity vector from the swimmer's velocity vector:
Swimmer's velocity vector - Stream's velocity vector = Resultant vector
So, 2 km/h - 1 km/h = 1 km/h
This result indicates that the swimmer should aim to swim at a velocity of 1 km/h in the opposite direction of the stream's flow. This will allow the swimmer to cross the river straight, counteracting the effect of the stream's velocity.
Therefore, the swimmer should swim in the opposite direction to the stream's flow, at a velocity of 1 km/h.