A Red Cross helicopter delivers crates of medicine to a war-tornarea because of

Question

A Red Cross helicopter delivers crates of medicine to a war-tornarea because of the hilly terrain, the helicopter cannot safelyland. Instead, the helicopter must hover above the ground, whilesomeone drops the crates.

The crates are designed to withstand “impactvelocities” of up to 8.0 m/s.

a)     Assuming the crates are dropped from rest, what is the highest thehelicopter can be off the ground, such that the crates don’tbreak when they land?

b)     The helicopter pilot accidentally starts ascending before the lastcrate is dropped. As a result, the last crate is“dropped” when the copter is 9.0 meters off the groundand rising at 3.0 m/s. how much time passes between when the crategets dropped and when it lands?

c)       How fast is the crate frompart b) moving right before it hits the ground?

Explanation / Answer

        impact velocity, V = 8 m/s (a)     h = V2 / 2g         = 64 / ( 2 * 9.8 )= 3.27 m (b)     height , h = 9 m     initial velocity of the crate, U = - 3 m/s ( indownward direction )     S = U t + ( 1/2 ) at2        - h = U t - ( 1/2) g t2         - h = -3 t - 4.9 t2            h = 3 t + 4.9 t 2          4.9 t 2 + 3t - 9 = 0       by solving, t = 1.08 s (c)     V = U + a t = - 3 - ( 9.8 * 1.08 )                       = - 13.58 m/s ( in downward direction )

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