(Figure 5.11) shows two positions `A and B` at the same height `h` above the ground. If the maximum height os the projectile is `H`, then determine the time `t` elapses between the positions `A and B` in terms of `H`.
.

Options

A. `sqrt((8)/(g)(H-h))`
B. `sqrt((8H)/(g))-sqrt((8h)/(g))`
C. `sqrt((8)/(g))sqrt((H^(2)-h^(2)))`
D. None

Answer

A

Explanation

Let T be the time of flight. We can now write `T=(2usintheta)/(g)`
`T^(2)=(4u^(2)sin^(2)theta)/(g^(2))=(8)/(g)((u^(2)sin^(2)theta)/(2g))=(8H)/(g)`
Hence, we can write in similar way, `t^(2)=(8(H-h))/(g)`