You wish to swim across a small river to your friend on the other side. The river is 30 m wide and you begin to swim straight across it at a speed of 1 m/s. The current in the river is 0.5 m/s and so the river carries you downriver as you swim. How far downriver in meters are you when you get to the other side?

Question

You wish to swim across a small river to your friend on the other side. The river is 30 m wide and you begin to swim straight across it at a speed of 1 m/s. The current in the river is 0.5 m/s and so the river carries you downriver as you swim. How far downriver in meters are you when you get to the other side?

Answer 1

as in 1sec he covers a distance of metre so in 30 sec he covers the whole river that is 30 m.

as there downstream also in 30 sec you cover a distance of 15 m in downstrem

you can do this thereodically

Answer 2

33.54 is incorrect

Answer 3

15 m downriver

Answer 4

To find out how far downriver you are when you get to the other side, we can use the concept of relative velocity. The relative velocity is the vector sum of your velocity (1 m/s in this case) and the velocity of the river current (0.5 m/s in this case).

Since you are swimming straight across the river and the current is flowing downstream, the relative velocity will have two components: one for your motion directly across the river and one for the motion caused by the current.

The component of the relative velocity that corresponds to your motion directly across the river is equal to your speed: 1 m/s. This component will help you reach the other side.

The component of the relative velocity that corresponds to the motion caused by the current is equal to the speed of the current: 0.5 m/s. This component will carry you downstream.

Since you are swimming straight across the river, the downstream distance you travel can be calculated using the equation:

Downstream distance = Time * Velocity

The time taken to cross the river can be obtained by dividing the width of the river by the component of the relative velocity that corresponds to your motion directly across the river:

Time = Width of the river / Velocity across the river

Substituting the given values, we get:

Time = 30 m / 1 m/s = 30 s

Now, we can calculate the downstream distance:

Downstream distance = Time * Velocity downstream

Downstream distance = 30 s * 0.5 m/s = 15 m

So, when you get to the other side, you will be 15 meters downriver due to the current.