There is a 250-m-high cliff at Half Dome in Yosemite National Park in California. Suppose a boulder breaks loose from the top of this cliff. (a) How fast will it be going when it strikes the ground? (b) Assuming a reaction time of 0.300 s, how long will a tourist at the bottom have to get out of the way after hearing the sound of the rock breaking loose (neglecting the height of the tourist, which would become negligible anyway if hit)? The speed of sound is 335 m/s on this day.
We are given the following values:
We solve for the velocity at the bottom of the cliff using the equation
or we can rewrite it as
Substitute the given values
The boulder is traveling at about 70 m/s downward when it strikes the ground.
Let be the time for the sound to travel to the tourist
Let be the total time before the tourist can react
Let be the time it takes the rock to reach the bottom
Now, subtract the times
The tourist has to get out of the way in 6.10 seconds.