Question

An American Red Cross plane needs to drop emergency supplies to victims of a hurricane in a remote part of the world. The plane is traveling horizontally at 100.0 m/s at a height of 50.0 m above the ground. What horizontal distance does the package travel before striking the ground?

Answer 1

This problem requires that you distinguish between perpendicular axes of motion. Motion along perpendicular axes does not have any dependence on the other axis.

In this case, you need to start by solving for how long it takes for the package to hit the ground. Time taken to hit the ground is only dependent on vertical motion. In this case, the package has no initial vertical velocity. The force acting on the package when it drops is gravity, so gravitational acceleration under free fall conditions will apply.

Free fall is governed by: h = 0.5 * g * t^2

You can use the free fall equation with gravitational acceleration 'g' and height 'h' to solve for the time taken to fall 't'.

After find the time 't', you can then use this time to figure out how far the package will travel horizontally. You know the package is initially moving at the same speed as the plane (100 m/s). After releasing the package, there is no force (neglecting air resistance) that will affect this velocity, so it will remain at 100 m/s. Therefore, we simply need to calculate the distance traveled for the package moving at a given speed for a set time.

Distance is simply calculated by: x = v * t

x will be the horizontal distance the package travels.