Question

A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4 m/s due east. The river is 800 m wide. How much time is required to cross the river?

• A. 187.6 s
• B. 400 s
• C. 173.91 s
• D. 200 s

Answer 1

The correct option is D

200 s

${\overrightarrow{v}}_m={\overrightarrow{v}}_{mr}+{\overrightarrow{v}}_r=4\hat{i}-2\hat{j}$

To calculate time, we need to consider only the horizontal displacement.

$\therefore d=800m$

$\therefore t=\frac{d_x}{v_x}$ is his horizontal component of velocity,

$\therefore t=\frac{800}{4}=200s$