n Cape Canaveral, Florida, the space shuttle Discovery launches on February 6, 2

Question

n Cape Canaveral, Florida, the space shuttle Discovery launches on February 6, 2016 in its final mission to the moon before being decommissioned and relocated to its final resting place in the Aeronautical Museum. Sometime after launch the space shuttle detaches its booster rockets and continues its journey toward the moon. Upon detachment, the boosters drop back toward Earth. As they drop back to Earth from rest they cover 3/4 the distance in the final 8 seconds in free fall. (a) What is the distance from earth to the height of detachment? (b) What was the total time the boosters were in free fall? In other words, how long did it take the boosters to splash into the ocean?

Explanation / Answer

let the total time be t and total height be h

h=0.5gt2= 4.9t2

h - 3h/4   = 4.9 (t-8)2

h/4= 4.9 (t-8)2

4.9t2/4 = 4.9 (t-8)2

t2/4 = (t-8)2

t/2= t-8

t=16s

h=4.9t2=4.9*162=1254.4m

hence (a)height=1254.4m (b) total time =16 seconds

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