Answer:
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:
[tex]v_{f} ^{2} -v_{0} ^{2} = 2* g* H (1)[/tex]
- If vf=0, if we assume that the positive direction is upwards, we can find the value of H as follows:
[tex]H = \frac{v_{0} ^{2} }{2*g} (2)[/tex]
- We can use the same equation, to find the value of D, as follows:
[tex]v_{f} ^{2} -v_{1} ^{2} = 2* g* D (3)[/tex]
- 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:
[tex](4*v_{0})^{2} - (-v_{0}) ^{2} = 2* g* D\\ \\ 15*v_{0}^{2} = 2*g*D[/tex]
[tex]D = \frac{15*v_{0} ^{2} }{2*g}[/tex]
- From (2) we know that H can be expressed as follows:
[tex]H = \frac{v_{0} ^{2} }{2*g}[/tex]
[tex]\frac{D}{H} = 15[/tex]
