Question

Assuming zero friction, what is the iniital velocity of a projectile that is fired straight up from the ground and takes 8 seconds to hit the ground.

Answer 1

Task. Assuming zero friction, what is the initital velocity of a projectile that is fired straight up from the ground and takes 8 seconds to hit the ground.

Solution. We should find the initial velocity $v_{0}$ of the projectile.

Notcie that the projectile moved with constant acceleration $g=9.8\;m/s^{2}$, and so the height of the projectile at time $t$ is given by the formula

$h(t)=v_{0}t-\frac{gt^{2}}{2}.$

By assumption the projectile hit the ground after 8 seconds, that is $h(8)=0$. Hence we get the following equation

$0=h(8)=v_{0}*8-\frac{g*8^{2}}{2}\qquad\Rightarrow\qquad 8v_{0}=\frac{64g}{2}=32g,$

and so

$v_{0}=4g=4*9.8=39.2\;m/s.$

Answer. $39.2\;m/s$.