Question

An object is dropped from a platform 100 feet high. Ignoring wind resistance, what will its speed be when it reaches the ground?

_____ ft/s

Answer 1

Task. An object is dropped from a platform 100 feet high. Ignoring wind resistance, what will its speed be when it reaches the ground?

Solution. There is a gravitation force acting on the object. Therefore it moves with constant acceleration $g=9.8\;m/s^{2}$. Since it was dropped, its initial velocity is zero. Therefore its height at time $t$ is given by the formula:

$h(t)=h_{0}-\frac{gt^{2}}{2},$

where $h_{0}=100$ feet is the initial height. We should find $t$ such that $h(t)=0$, that is

$h_{0}-\frac{gt^{2}}{2}=0$

$t^{2}=\frac{2h_{0}}{g}.$

$t=\sqrt{\frac{2h_{0}}{g}}.$

Notice that

$1\;\mathrm{foot}=0.3048\;m,$

so

$h_{0}=100\;\mathrm{feet}=304.8\;m.$

Therefore

$t=\sqrt{\frac{2h_{0}}{g}}=\sqrt{\frac{2*304.8}{9.8}}=\sqrt{\frac{609.6}{9.8}}=\sqrt{62.204}=7.8870\approx 7.9\;s.$

Answer. 7.9 s.