To calculate the time elapsed before the diver reaches the water, we can use the kinematic equation that relates the final velocity (vf), initial velocity (vi), acceleration (a), and displacement (d):
vf^2 = vi^2 + 2ad
In this case, the initial velocity (vi) is 0 m/s because the diver starts from rest at the top of the cliff. The displacement (d) is the height of the cliff, which is 50 m. The final velocity (vf) is 60 m/s, and the acceleration (a) due to gravity is approximately 9.8 m/s^2.
Plugging in the values into the equation:
60^2 = 0^2 + 2 * 9.8 * 50
3600 = 2 * 9.8 * 50
3600 = 980 * 50
3600 = 49000
Now, we can solve for time (t):
t = sqrt(2d/a)
t = sqrt(2 * 50 / 9.8)
t = sqrt(100 / 9.8)
t = sqrt(10.204)
t ≈ 3.2 seconds
Therefore, approximately 3.2 seconds had elapsed before the diver reached the water.