Question

A football is kicked vertically upward from the ground and a student gazing out of the window sees it moving upward past her at velocity U. The window is a height h above the ground. You may ignore air resistance. How high does the football go above ground?

Answer 1

Answer:

$H = \frac{u^2}{2g} + h$

Explanation:

Let the football is kicked up vertically with some speed given as

$v = v_o$

now its speed when it will reach to height "h" above the ground is given as "u"

so we will have

$v_f^2 - v_i^2 = 2 a d$

here we have

$u^2 - v_o^2 = 2(-g)h$

so we have

$v_o^2 = u^2 + 2gh$

now we know that when football will reach to maximum height then it will have zero final velocity

So we will have

$v_f^2 - v_i^2 = 2 a s$

$0 - (u^2 + 2gh) = 2(-g)H$

so we have maximum height given as

$H = \frac{u^2 + 2gh}{2g}$

$H = \frac{u^2}{2g} + h$