Problem: 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?

FREE Expert Solution

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:

  1. Identify the target variable  and known variables for each direction—remember that only 3 of the 5 variablesx or Δy, v0, vf, a, and t) are needed for each direction. Also, it always helps to sketch out the problem and label all your known information!
  2. Choose a UAM equation—sometimes you'll be able to go directly for the target variable, sometimes another step will be needed in between.
  3. Solve the equation for the target (or intermediate) variable, then substitute known values and calculate the answer.

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:

 vf = v0 +atx= (vf+v02)tx= v0t+12at2 vf2= v02 +2ax

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.)

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Problem Details

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?