Answer to Question #168824 in Physics for Hannah

Question

A large stone is dropped vertically down word from a cliff overlooking the ocean if the sound of the stone hitting the water is heard 3 point40 seconds later and you know that the speed of the sound is 340 m/s how high is the cliff

Answer 1

Let's first find the time that the stone takes to reach the water:

$$h=\dfrac{1}{2}gt_1^2,$$ $$t_1=\sqrt{\dfrac{2h}{g}}.$$

Then, we can write the time that the sound of splash takes to reach the person's ear:

$$t_2=\dfrac{h}{v}=\dfrac{h}{340}.$$

The total time can be found as follows:

$$t=t_1+t_2,$$ $$\sqrt{\dfrac{2h}{g}}+\dfrac{h}{340}=3.40,$$ $$9.8h^2+253857.6h-13096092.8=0.$$

This quadratic equation has two roots: $h_1=25852\ m$ and $h_2=51.69\ m.$ The correct answer is $h=51.69\ m$.

Answer:

The height of the cliff is 51.69 m.