Question

A ball is thrown vertically upward with initial velocity v. Find the maximum height H of the ball as a function of v. Then find the initial velocity v required to achieve a height of H.

gravity in this case will be 32ft/s^2
h=-(1/2)32t^2 + vt.

Questions
1. Height H achieved with given initial velocity v:
2. Initial velocity v required to achieve given height H:

Answer 1

A ball is thrown vertically upward with initial velocity v. Find the maximum height H of the ball as a function of v.
so the H is:

h = -(1/2)gt^2 + vt.
where g = 32 ft/s^2 or 9.8 m/s^2

so the initial velocity can be solve by rearranging the equation

h = -(1/2)gt^2 + vt.
h + (1/2)gt^2 = vt
v = h/t + (1/2)gt