Question

A man crosses the river perpendicular to river flow in time t seconds and travels an equal distance down the stream in T seconds. The ratio of man's speed in still water to the speed of river water will be :

• A. $\frac{t^{2}–T^{2}}{t^{2} + T^{2}}$
• B. $\frac{T^{2}–t^{2}}{T^{2} + t^{2}}$
• C. $\frac{t^{2} + T^{2}}{t^{2}–T^{2}}$
• D. $\frac{T^{2} + t^{2}}{T^{2}–t^{2}}$

Answer 1

Answer: (C)

$\frac{t^{2} + T^{2}}{t^{2}–T^{2}}$

Answer 2

Let velocity of man in still water be v and that of water with respect to ground be u.

Velocity of man perpendicular to river flow with respect to ground = $\sqrt{v^{2}–u^{2}}$

Velocity of man downstream = v + u

As given. $\sqrt{v^{2}–u^{2}}$t = (v + u)T

⇒ (v² – u²)t² = (v + u)² T²

⇒ (v – u)t² = (v + u)T²

∴ $\frac{v}{u}$ = $\frac{t^{2} + T^{2}}{t^{2}–T^{2}}$