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?

Options

A. The angle made by the boat with the shore is `53^(@)`
B. The angle made by the boat with the shore is `37^(@)`
C. the time taken by boat to reach the child is `4 min`
D. the time taken by boat to reach the child is `3 min`

Answer

B, D

Explanation

`vecv_(b)="velocity of boatman"=vecv_(br)+vecv_(r)`
`vecv_(c)="velocity of child"=vecv_(r),vecv_(bc)=vecv_(b)-vecv_(c)=vecv_(br)`
`vecv_(br)` should be along `BC` i.e, `vecv_(br)` should be along
`BC`, where `tan alpha=0.6/0.8=3/4,alpha=37^(@)`
Further, `t=(BC)/(|vecv_(br)|)=1/20hr =3` minute