Final answer:
The boulder will be going approximately 70.7 m/s when it strikes the ground. The tourist will have approximately 0.746 seconds to get out of the way after hearing the sound of the rock breaking loose.
Step-by-step explanation:
To answer the first part of the question, we can use the principle of conservation of energy. The potential energy of the boulder at the top of the cliff is converted into kinetic energy as it falls. We can use the equation:
mgh = 0.5mv^2
where m is the mass of the boulder, g is the acceleration due to gravity (9.8 m/s^2), h is the height of the cliff (250 m), and v is the final velocity of the boulder.
Simplifying the equation, we get:
v = sqrt(2gh)
Substituting the known values, we find:
v = sqrt(2 * 9.8 * 250) ≈ 70.7 m/s
So, the boulder will be going approximately 70.7 m/s when it strikes the ground.
To answer the second part of the question, we need to calculate the time it takes for the sound of the rock breaking loose to reach the tourist at the bottom of the cliff. We can use the formula:
d = st
where d is the distance traveled by the sound (250 m), s is the speed of sound (335 m/s), and t is the time it takes for the sound to reach the tourist.
Plugging in the known values, we get:
250 = 335t
Solving for t, we find:
t = 250/335 ≈ 0.746 s
Therefore, the tourist will have approximately 0.746 seconds to get out of the way after hearing the sound of the rock breaking loose.