Question

A Ship floats on water send a sound when it was 900 m away from a mountain & hears a sound after 6 seconds if the velocity of the sound was 340 m/sec find the velocity of the ship .

Answer 1

A Ship floats on water send a sound when it was 900 m away from a mountain & hears a sound after 6 seconds if the velocity of the sound was 340 m/sec and the velocity of the ship.

Ship will hear a sound after time:

$$t = \frac {s}{c _ {s}} + \frac {s - \Delta s}{c _ {s}} = \frac {2 s - \Delta s}{c _ {s}} \rightarrow \Delta s = 2 s - c _ {s} t$$

A ship will pass distance $\Delta s$ during the same time $t$

$$v = \frac {\Delta s}{t}$$ $$v = \frac {2 s - c _ {s} t}{t} = \frac {2 s}{t} - c _ {s}$$ $$v = \frac {2 * 9 0 0 m}{6 s} - 3 4 0 m / s = - 4 0 m / s$$

Sign “-” means that ship moves away from the mount.

Answer: $v = 40 \, \text{m/s}$ away from the mount