Question

A river 500 m wide is flowing with a current of 4 kh A boat starts from one bank of the river wishes to cross the river at right angle to stream direction. Boatman can row the boat at 8 kph. If the time taken by the man to the river is $\frac{5n}{2\sqrt{3}}$ min then value of n is

Answer 1

Let $V_r$ be the velocity of current of river and $V_b$ be the velocity of the boat.Time taken to cross the river:

$t=\frac{5n}{2\sqrt{3}\times 60}h$

$8t=\sqrt{(0.5{)}^2+(4t{)}^2}$

$8t=\sqrt{0.25+16t^2}$

$64t^2=0.25+16t^2$

$t^2=\frac{0.25}{48}$

$t=\sqrt{\frac{0.25}{48}}=\frac{5n}{2\sqrt{3}\times 60}$

$n=3$