Question

a boat which can move with a speed of 5m/s relative to water crosses a river of width 480m flowing with a constant speed of 4m/s. what is the time taken by the boat to cross the river along the shortest path​

Answer 1

time taken by boat to cross the river along shortest path , t = $\frac{d}{\sqrt{v^2-u^2}}$

where d is width of river , v is speed of boat relative to river and u speed of river.

given,

speed of river, u = 4m/s

speed of boat with respect to river, v = 5m/s

and width of river, d = 480m

now, time taken to cross the river , t = 480/√(5² - 4²)

= 480/√(25 - 16) = 480/3 = 160sec or, 2min 40 sec

hence, time taken to cross the river along shortest path is 2min 40sec.