Question

A water surfer is moving at a speed of 15 m/s. When he is surfing in the direction of wave, he swingsupwards every 0.8 s because of wave crests. While surfing in opposite direction to that of wave motion, he swings upwards every 0.6 s. Determine the wavelength of transverse component of the water wave.

• A. 15 m
• B. 10.3 m
• C. 21.6 m
• D. Information insufficient

Answer 1

The correct option is B 10.3 m

Let the speed of wave be v, for crossing one wave crests to the other while travelling in the same direction, the surfing speed has to be greater than speed of the wave, i.e.,v < 15 m/s.
Let wavelength of wave be $\lambda m$
While surfing in the same direction,
$\lambda =(15-v)\times 0.8$
While surfing in the direction opposite to the wave motion,
$\lambda =(15+v)\times 0.6$
(15 - v)0.8 = (15 + v)0.6
$v=\frac{15}{7}m/s=2.143m/s$
So, $\lambda =(15-2.143)\times 0.8=10.3m$