A small airplane flying horizontally with a speed of 180 mi/hr at an altitude of

Question

A small airplane flying horizontally with a speed of 180 mi/hr at an altitude of 400 ft
above a remote valley drops an emergency medical package at A.

A small airplane flying horizontally with a speed of 180 mi/hr 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 the 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 atmospheric resistance from A to B 180 mi/hr 400 Target

Explanation / Answer

here,

speed of the airplane ,u = 180 mi/hr

u = 80.47 m/s

altitude , A = 400 ft = 121.92 m

vertcial constant speed of parachute , vp = 6 ft/s = 1.83 m/s

let the height of point B be h and time taken to reach be t1

total time taken , t = 37 s

(A - h) = 0 + 0.5 * g * t1^2

121.92 - h = 4.9 * t1^2 ....(1)

after point B let the time taken be t2

t2 = t - t1 = 37 - t1

and

vp * t2 = h

1.83 * ( 37 - t1) = h ....(2)

from (1) and (2)

h = 61.27 m , t1 = 3.52 s

the horizontal lead , L = u * t1

L = 283.25 m

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