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A river is flowing with a speed of 1 km ...

A river is flowing with a speed of `1 km h^-1` A swimmer wants to go point `C` starting from `A`. He swims with a speed of `5 km h^-1` at an angle `theta` w.r.t. the river flow. If `AB = BC = 400 m`, at what angle with the river bank should the swimmer swim ?
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Text Solution

Verified by Experts

Resultant path of the swimmer is at `45^@` with bank, therefore, x - and y - components of swimmer's resultant velocity must be equal.
Let velocity of swimmer `|vec v_m| = v`
`v_x = v_r + v_(m,r) cos theta`
`v_y = v_(m,r) sin theta`
Condition for reaching the point `C`,
`tan 45^@ = (v_y)/(v_x), v_y = v_x`
`(v_r + v_(m,r) cos theta) = v_(m,r) sin theta`
`1 + 5 cos theta = 5 sin theta`
On squaring, `1 + 25 cos^2 + 10 cos theta = 25 - 25 cos^2 theta`
`50 cos^2 theta + 10 cos theta - 24 = 0`
On solving, we get `theta = 53^@`.
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