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Projectile Motion Problem & Solution

Problem

A student sits atop a platform a distance h above the ground. He throws a large object horizontally with a speed u. A wind blowing parallel to the ground gives the object a constant horizontal acceleration with magnitude a. This results in the object reaching the ground directly under the student. Determine the height h in terms of u, a and g. Ignore the effect of air resistance on the vertical motion.

Solution

Image(2)

For vertical motion,

$h = \frac{1}{2}g{t^2}$............*

For horizontal motion,

$0 = ut + \frac{1}{2}( - a){t^2}$

or $0 = u - \frac{1}{2}at$..............#

Putting $t = \sqrt {\frac{{2h}}{g}}$ from * in #,

$0 = u - \frac{1}{2}a\sqrt {\frac{{2h}}{g}}$

or $h = \frac{{2{u^2}g}}{{{a^2}}}$.

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