Question

If the maximum distance you can throw a ball over horizontal ground is xmax, what's the greatest height h you can throw it vertically?

Answer 1

a/c to question, I can throw a ball over horizontal ground is $x_{max}$

we know, formula of horizontal range is given by, $R=\frac{u^2sin2\theta}{g}$

where, u is initial velocity of body.

maximum range, $x_{max}$ will be possible only when $sin2\theta=1$

or, $\theta=45^{\circ}$

e.g., $x_{max}=\frac{u^2}{g}$.....(1)

now, maximum height , h = $\frac{u^2sin^245^{\circ}}{2g}$

= $\frac{u^2}{4g}$

from equation (1),

so, $h=\frac{x_{max}}{4}$