EXPLANATION
Let's see the facts:
Maximum height = 64 feet Time = 2 seconds
Time to hit the ground = 4 seconds
Gravity = 9.8 m/s^2
The position equation is as follows:
[tex]\text{Position}=\frac{1}{2}\cdot aceleration\cdot time^2+velocity\cdot time+initial\text{ position}[/tex]Representing this situation:
Time to reach peak=
[tex]velocity\text{ }+\text{ aceleration}\cdot time=0[/tex]Replacing terms:
[tex]initial\text{ velocity-}9,8\cdot2=0[/tex]Isolating the initial velocity:
[tex]\text{Initial velocity=9}.8\frac{m}{s^2}\cdot2s=19.6\frac{m}{s}[/tex]Now, we now that at first segment, the ball travel 64 feet to the maximum height, thus we have a height of 64 feet. Now, we need to compute the distance to the ground applying the free fall kinematic equation.
[tex]\text{Distance traveled from the top=}\frac{1}{2}\cdot g\cdot t^2[/tex]As the time elapsed from the top was 4 seconds, the equation would be:
[tex]\text{Distance trave}led\text{ from the top=}\frac{1}{2}\cdot9,8\cdot4^2[/tex]Multiplying numbers and computing the powers:
[tex]\text{Distance traveled from the top=}78.4\text{feet}[/tex]Now, we need to subtract the distance traveled from the top to the maximum height reached in order to obtain the height:
[tex]\text{Height of the cliff=Distance traveled from the top-Max}imum\text{ height reached}[/tex]Replacing terms:
[tex]\text{Height of the cliff=78.4 f}eet-64\text{ fe}et\text{ = 14.4 fe}et[/tex]The cliff is 14.4 feet tall
