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 3.00 m/s2 . When it is 245 m 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).

How high is the rocket when the canister hits the launch pad, assuming that the rocket does not change its acceleration? What total distance did the canister travel between its release and its crash onto the launch pad?

Explanation / Answer

for rocket

initial velocity

voy = 0

acceleration ay = 3 m/s^2

diplacement y = 245 m

velocity at y position = vy

vy^2 - voy^2 = 2*ay*y

vy^2 - 0 = 2*3*245

vy = 38.34 m/s

for canister

along vertical

initial velocity v2y = 38.34 m/s

acceleration ay = -g = -9.8 m/s^2

displacement y = -245 m

y = v2y*t + (1/2)*ay*t^2

-245 = 38.34*t - (1/2)*9.8*t^2

t = 12 s

distance travelled by rock in time t = 12 s time

y = v2y*t + (1/2)*ay*t^2

y = 38.34*12 + (1/2)*3*12^2 = 676.1 m

the rocket is at aheight h = 245 + 676.1 = 921.1 m

-------------------------

maximum height reached by canister hmax = v2y^2/(2g) = 38.34^2/(2*9.8) = 75 m

total distance = 75 + 75 + 245 = 395 m

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