During launches, rockets often discard unneeded parts. A rocket starts from rest

Question

During launches, rockets often discard unneeded parts. A rocket starts from rest on the launch pad and accelerates upward at a steady acceleration of 5 times that of g. When it is 300 m above the launch pad, it discards a used fuel canister by simply disconnecting it. Once disconnected, the only force acting on the canister is gravity.

a. Determine the maximum height reached by the canister, after separating from the rocket

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

Explanation / Answer

(a) Rocket starts from rest, so initial velocity vo = 0 m/s

acceleration = ao = 5g in upward direction

Distance travelled = yo = 300 m

Final velocity after travelling 300 m = v = ?

Using v^2 = vo^2 + 2aoyo

v^2 = 0 + 2( 5 x 9.81)(300)

v = 121.3 m/s

Now rocket moves under the influence of gravity only.

Let maximum height reached = y

acceleration = a = -9.81 m/s^2

final velocity on reaching maximum height = v’ = 0 m/s

Using

v’^2 = v^2 + 2ay

0 = 121.3^2 + 2(-9.81)y

y = 749.9 m

(b) Total distance covered during upward motion = 300 m + 749.9 m = 1049.9 m

Total distance covered during downward motion = Total distance covered during upward motion = 1049.9 m

Total distance the canister travels between its release and its crash onto the launch pad = 1049.9 m + 1049.9 m = 2099.8 m

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