A diver running 1.89 m/s dives out horizontally from the edge of a vertical cliff and 2.88 s later reaches the water below. How high was the cliff.
(in m)
h = Vo*t + 0.5g*t^2
Vo = 0
t = 2.88 s.
g = 9.8 m/s^2
Solve for h.
To find the height of the cliff, we can use the equation of motion. The equation we are interested in is:
h = (1/2) * g * t^2
where:
h is the height of the cliff,
g is the acceleration due to gravity (approximately 9.8 m/s^2), and
t is the time taken for the diver to reach the water.
We are given that the diver ran horizontally, meaning their initial vertical velocity is 0 m/s. Given this information, the time it takes for the diver to reach the water is the same as the time it takes for the object to fall from rest. Therefore, it gives us the time needed for freefall.
Substituting the given values into the equation:
h = (1/2) * 9.8 m/s^2 * (2.88 s)^2
h = (1/2) * 9.8 m/s^2 * 8.2944 s^2
h = 40.37616 m
Therefore, the height of the cliff is approximately 40.38 m.