A man in a boat crosses a river from point A. If he rows perpendicular to the banks he reaches point C `(BC = 120 m)` in 10 min. If the man heads at a certain angle `alpha` to the straight line AB (AB is perpendicular to the banks) against the current he reaches point B in 12.5 min. Find the width of the river w, the rowing velocity u, the speed of the river current v and the angle `alpha`. Assume the velocity of the boat relative to water to be constant and the same magnitude in both cases.

Options

A. The width of the river is `300m`
B. The width of the river is `200m`
C. The rowing velocity is `20m//min`
D. The rowing velocity is `30m//min`

Answer

B, C

Explanation

In the first case `BC=vt_(1)` and `w=ut_(1)`.In the second caste `u sin alpha=v` and `w=u cos alpha1/2`
Solving these four equations with proper substitution, we get `w=200m,u=20m//min,v=12 m//min` and `alpha~=37^(@)`