A bal is launched upward with a velocity of v0 from the edge of a cliff of height D. it reaches a maximum height of H above its launch, then falls back downward and misses the edge of the cliff, landing below, at the bottom of the cliff, with a speed of 4V0. What is the ratio of the cliff height D to the peak height H

D/H =15

Explanation:

We can find first the peak height H, taking into consideration, that at the maximum height, the ball will reach momentarily to a stop.At this point, we can find the value of H, applying the following kinematic equation:

       

If vf=0, if we assume that the positive direction is upwards, we can find the value of H as follows:

       

We can use the same equation, to find the value of D, as follows:

       

In order to find v₁, we can use the same kinematic equation that we used to get H, but now, we know that v₀ = 0.When we replace these values in (1), we find that  v₁ = -v₀.Replacing in (3), we have:

       

Solving for  D:

       

From (2) we know that H can be expressed as follows:

       

⇒ D = 15 * H