Question

A man wishes to cross the river flowing with velocity \(v\) making angle \(\theta\) with y direction. If he swims with speed \(u\) and width of river is \(d\), the time taken will be

• A. \(\dfrac{d}{u+v\cos\theta}\)
• B. \(\dfrac{d}{u-v\cos\theta}\)
• C. \(\dfrac{d}{u\cos\theta}\)
• D. \(\dfrac{d}{v\sin\theta}\)

Hint:

For river crossing, \(v\) changes landing point, \textbf{not} the time.

Answer 1

The Correct Option is C

Step 1: To cross the river, only the component of velocity perpendicular to the bank is useful.
Step 2: Effective crossing speed: \[ u_{\perp}=u\cos\theta. \]
Step 3: Time to cross width: \[ t=\frac{d}{u\cos\theta}. \]
Step 4: Flow velocity \(v\) affects drift, not crossing time. Hence → (C).