Answer to Question #167479 in Physics for Froilan

Question

Glenda drops a coin from ear-level down a cliff at standard temperature and pressure. The coin falls a distance of 440 m before it strikes the water. How long after Glenda releases the coin will she hear a splash?

Answer 1

Let's first find the time that the coin takes to reach the surface of water:

$$y=\dfrac{1}{2}gt_1^2,$$ $$t_1=\sqrt{\dfrac{2y}{g}}=\sqrt{\dfrac{2\cdot440\ m}{9.8\ \dfrac{m}{s^2}}}=9.47\ s.$$

Then, we can find the time that the sound of a splash takes to reach Glenda's ear (the speed of sound at standard temperature and pressure equals $343\ \dfrac{m}{s}$):

$$t_2=\dfrac{y}{v}=\dfrac{440\ m}{343\ \dfrac{m}{s}}=1.28\ s.$$

Finally, we can find the total time that takes from releasing the coin until Glenda hear the splash of water:

$$t=t_1+t_2=9.47\ s+1.28\ s=10.75\ s.$$