In this problem, we're asked to calculate the time when a plane should drop supplies to land on a target, given the plane's initial velocity and the height the package is dropped from.
For projectile motion problems in general, we'll follow these steps to solve:
If something is dropped from a horizontally moving vehicle, that means v0x is the same as the vehicle's velocity, and v0y=0. Basically, we can solve this in exactly the same way as a horizontal launch problem.
The four UAM (kinematics) equations are:
We define our coordinate system so that the +y-axis is pointing upwards and the +x-direction is horizontal along the launch direction. That means ay = −g, and ax = 0 (because the only acceleration acting on a projectile once it's launched is gravity.)
The pilot of an airplane traveling 170 km/h wants to drop supplies to flood victims isolated on a patch of land 160 m below. Assume the plane is moving purely horizontally.
The supplies should be dropped how many seconds before the plane is directly overhead?