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.

Answer

A, B, C

Explanation

In the first case, `BC= vt_1 and w=ut_1`

In the second case,
`u sin alpha = v and w= (u cos alpha) t_2`
Solving these four equations with proper substitutions, we get
`w=200m,`
`u= 20 m//min,`
`v= 12 m//min`
and `alpha = 36^@50^'`