A student drops a stone from the edge of a sea cliff. The sound of the stone striking the ocean is heard 3.8s after the stone is released. The speed of sound in air is 340m/s. Find the height of the cliff. Ignore air resistance.
h = 1/2 g t^2 = 4.9 t^2
t + (h / 340) = 3.8 ... h = 340 (3.8 - t) = (340 * 3.8) - 340 t
substituting ... 4.9 t^2 + 340 t - 1292 = 0
solve for t , substitute back to find h
To find the height of the cliff, we need to use the equation of motion for free fall. The equation is:
h = 0.5 * g * t^2
where h is the height of the cliff, g is the acceleration due to gravity, and t is the time it takes for the stone to hit the water.
First, we need to find the time it takes for the stone to fall by subtracting the time it takes for the sound to reach us from the total time. In this case, the time for sound to reach us is 3.8 seconds.
So, the time for the stone to fall is:
t = total time - time for sound = 3.8 seconds - 0 seconds = 3.8 seconds
Next, we need to substitute the value of t into the equation of motion:
h = 0.5 * g * t^2
The acceleration due to gravity, g, is approximately 9.8 m/s^2.
h = 0.5 * 9.8 m/s^2 * (3.8 s)^2
h = 0.5 * 9.8 m/s^2 * 14.44 s^2
h = 70.84 meters
Therefore, the height of the cliff is approximately 70.84 meters.