A child in danger of drowning in a river is being carried downstream by a current that flows uniformly at a speed of `2.5 km//h.` The child is 0.6 km from shore and 0.8 km upstream of a boat landing when a rescue boat sets out. If the boat proceeds at its maximum speed of `20 km//h` with respect to the water, what angle does the boat velocity v make with the shore? How long will it take boat to reach the child?

Answer

C

Explanation

`v_b` = velocity of boatman = `v_(br) + v_r`
and `v_c `= velocity of child = `v_r`
`:. v_(bc) = v_b - v_c = v_(br)`
`v_(bc)` should be along BC.
i.e. `v_(br)` should be along BC,
where, `tan alpha = 0.6/0.8 = 3/4`
or `alpha=37^@`

Further `t=(BC)/|v_(br)| =1/20 h`
`=3` min