Question

Madelin fires a bullet horizontally. The rifle is 1.4 meters above the ground. The bullet travels 168 meters horizont before it hits the ground. What speed did Madelin's bullet have when it exited the rifle?

Answer 1

The position vector of the bullet has components

$x=v_0t$

$y=1.4\,\mathrm m-\dfrac g2t^2$

The bullet hits the ground when $y=0$, which corresponds to time $t$:

$1.4\,\mathrm m-\dfrac g2t^2=0\implies t=0.53\,\mathrm s$

The bullet travels 168 m horizontally, which would require a muzzle velocity $v_0$ such that

$168\,\mathrm m=v_0(0.53\,\mathrm s)$

$\implies v_0\approx320\,\dfrac{\mathrm m}{\mathrm s}$