Question

During launches, rockets often discard unneeded parts. A certain rocket starts from rest on the launch pad and accelerates upward at a steady 3.20 m/s2 . When it is 250 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).

Part A

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

Answer 1

a) The time is, t = squareroot 2h/g = squareroot 2(250)/9.8 = 7.14 s The velocity at time is, v^2 - u^2 = 2as v^2 - 0 = 2as v = squareroot 2as = squareroot 2(3.2)(250) = 40 m/s The total distance travelled after that disconnection is, s = (40)(7.14) + 1/2 (3.2)(7.14)^2 = 367 m So from ground surface rocket will be at distance is, d = 367 m + 250 m = 617 m