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Projectile Motion Problem & Solution


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.



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}}}.