Question

An airplane is flying horizontally at an altitude of 325m and velocity of 270m/s what distance before the drop target should we drop the package?

Answer 1

The equations of motion of the package are $y(t) = h - \frac{g t^2}{2}$, $x(t) = v_0 t$, where $h$ is the initial altitude, $v_0$ - initial velocity of the package.

Equating altitude to zero, one can find the time $T$ it will take to reach the ground: $0 = h - \frac{g T^2}{2} \Rightarrow T = \sqrt{\frac{2 h}{g}}$.

Therefore, the horizontal distance before dropping the package should be $L= x(T) = v_0 T = v_0 \sqrt{\frac{2 h}{g}} \approx 2197.8 m$.