A river is flowing at 3mps.A man can swim in still water at a speed of 6mps.The angle at which the bank at which the swimmer should start ,so that he may cross the river along the shortest distance is?

Say the river runs south

We want to end up going east

Our velocity north will be 6 cos T - 3 = 0
if T is angle from north
cos T = 1/2
T = 60 degrees from north which is 30 degrees from straight across

To find the angle at which the swimmer should start in order to cross the river along the shortest distance, we can use the concept of relative velocity.

Let's assume the river is flowing from left to right horizontally, and the swimmer wants to cross the river from left to right. The swimmer's speed in still water is 6 m/s, and the river is flowing at a speed of 3 m/s.

To minimize the distance the swimmer needs to swim, we need to find the direction in which the swimmer should aim so that the combination of their own velocity and the river's velocity will result in a diagonal path across the river.

Now, let's break down the swimmer's velocity into horizontal and vertical components. Since the swimmer can swim at a speed of 6 m/s in still water, the horizontal component of their velocity will be 6 m/s (since the river flow is in the same direction) and the vertical component will be 0 m/s (since there is no vertical flow in the river).

The river's velocity can be broken down into horizontal and vertical components as well. Since the river is flowing horizontally from left to right at 3 m/s, the horizontal component of the river's velocity will be 3 m/s and the vertical component will be 0 m/s (no vertical flow).

To find the resultant velocity, we add the corresponding components of the swimmer's and river's velocities. The horizontal component of the resultant velocity will be the sum of the swimmer's and river's horizontal velocities, which is 6 m/s + 3 m/s = 9 m/s. The vertical component remains unchanged at 0 m/s.

Now, we can determine the angle at which the swimmer should start by using trigonometry. The tangent of the desired angle is equal to the vertical component of the resultant velocity divided by the horizontal component:

tan(theta) = vertical component / horizontal component
tan(theta) = 0 m/s / 9 m/s
tan(theta) = 0

Since the tangent of any angle is 0, we can conclude that the angle at which the swimmer should start to cross the river along the shortest distance is 0 degrees (or 180 degrees in the opposite direction). The swimmer should aim directly across the river, parallel to the flow of the river.

Please note that this assumes the swimmer has the physical capability to swim at the said speed and in the said conditions. Safety precautions should always be taken when swimming in rivers or other bodies of water with currents.