Question

A child in danger of drowning in a river is being carried downstream by a current that flows uniformly at a speed of $2.5km/h$. The child is $0.6km$ from shore and $0.8km$ upstream of a boat landing when a rescue boat sets out. If the boat proceeds at its maximum speed of $20km/h$ with respect to the water, the angle (in degrees) , the boat velocity $v$ make with the shore is 37x. The value of x is:

Answer 1

Let boat velocity be v and we need to determine the angle boat makes with the shore.
${\overrightarrow{v}}_b=$ velocity of boatman ${\overrightarrow{v}}_{br}+{\overrightarrow{v}}_r$
and ${\overrightarrow{v}}_c=$ velocity of child $={\overrightarrow{v}}_r$
$\therefore {\overrightarrow{v}}_{bc}={\overrightarrow{v}}_b-{\overrightarrow{v}}_c={\overrightarrow{v}}_{br}$
${\overrightarrow{v}}_{br}$ should be along BC.
i.e., ${\overrightarrow{v}}_{br}$ should be along BC.
where, $tan\alpha =\frac{0.6}{0.8}=\frac{3}{4}$
or $\alpha ={37}^o$