During launches, rockets often discard unneeded parts. A certain rocket starts f

Question

During launches, rockets often discard unneeded parts. A certain rocket starts from rest on the launch pad and accelerates upward at a steady 3.20m/s^2. When it is 255m above the launch pad, it discards a used fuel canister by simply disconnecting it. Once it is disconnected, the only force acting on the canister is gravity. (Air resistance can be ignored)

a) How high is the rocket when the canister hits the launch pad, assuming that the rocket does not change its acceleration?

b) What total distance did the canister travel between its release and its crash onto the launch pad?

Please show work. Do not just copy paste from the internet. Thanks

Explanation / Answer

(a)

velocity of rocket at the time of disconnecting cannister , initial velocity is 0 and acceleration is 3.2 m/s2

from v2 = u2 +2as

v2 = 0 +2*3.2*255 = 1632

so v = 40.4 m/s

time taken by cannister to come to launch pad, its initial velocity is 40.4 and acceleration is g

from s = ut+0.5at2

255 = -40.4t +0.5*9.81*t2

4.9t2 -40.4t -255

t = 12.42 s

now it goes another 12.42s after this and cannister hit the launch pad , for here initial velocity is 40.4 m/s

so from s = ut + 0.5 a t2

s = 40.4*12.42 + 0.5*3.2*(12.42)2 = 748.58

so height of the rocket when cannister hit the launch pad is 255+748.58 = 1003.58 m

cannister first goes from velocity 40.4 to zero

distance travelled at this time interval

from v2 = u2 -2gs

s = 83.2 m

and it comes down another 83.2m at the same position and then it travels 255m to the launch pad

so total distance travelled = 83.2+83.2+255 = 421.4 m

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