Final answer:
To find the height of the cliff, we can use the kinematic equations for vertical motion. By plugging in the given values and solving the equations, we find that the height of the cliff is 37.2 meters.
Step-by-step explanation:
To find the height of the cliff, we can use the kinematic equation for vertical motion: vf = vo + gt, where vf is the final velocity, vo is the initial velocity, g is the acceleration due to gravity, and t is the time.
Given that the rock reaches a speed of 23.4 m/s just before hitting the ground, and the maximum altitude is reached in 1.59 seconds, we can determine the value of g by rearranging the equation as follows: g = (vf - vo)/t.
Substituting the values, we have: g = (23.4 - 0)/1.59.
Next, we can use the kinematic equation for vertical displacement: s = vo*t + (1/2)gt^2, where s is the displacement.
Since the rock is thrown vertically upwards, the initial velocity is equal to zero. Thus, the equation simplifies to: s = (1/2)gt^2.
Now, we substitute the known values into the equation: s = (1/2)*(23.4/1.59)*1.59^2.
After performing the calculations, we find that the height of the cliff is 37.2 meters.