A small airplane flying horizontally with a speed of 180 mph at an altitude of 4

Question

A small airplane flying horizontally with a speed of 180 mph at an altitude of 400 ft above a remote valley drops an emergency medical package at A. The package has a parachute which deploys at B and allows the package to descend vertically at a constant rate of 6 ft/s. If the drop is designed so that the package is to reach the ground 37 seconds after release at A, determine the horizontal lead L so that the package hits the target. Neglect air resistance.

A small airplane flying horizontally with a speed of 180 mph at an altitude of 400 ft above a remote valley drops an emergency medical package at A. The package has a parachute which deploys at B and allows the package to descend vertically at a constant rate of 6 ft/s. If the drop is designed so that the package is to reach the ground 37 seconds after release at A, determine the horizontal lead L so that the package hits the target. Neglect air resistance.

Explanation / Answer

let time taken to reach B is t.

1 mile/hr=1.467 ft/sec

so 180 mph=264 ft/sec

so 264*t=L....(1)

in t seconds,height descended=0.5*32*t^2=16*t^2

after that it takes 37-t seconds to reach the ground.

then height of B=6*(37-t)

so 16*t^2+6*(37-t)=400

solving for t,we get

t=3.528 sec

so L=264*t=931.4 ft

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