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A rocket is fired straight up It accelerates upward at 35 mss for 35 s then runs out of fuel Ignore any air resistance effects How long is the rocket in the air?
There are three phases to this calculation:
# The initial powered acceleration # The deceleration under gravity to the top of the trajectory # The acceleration under gravity back to the ground Using the equations:
a = 2(s - ut)/t2
a=(v-vo)/t
Phase 1
Acceleration (a) = 35m/s2
Time (t1) = 35s
Velocity(v) = 35 x 35 = 1,225m/s
Distance travelled (S1) = 21,437m
Phase 2
Acceleration (a) = -9.8m/s2
Initial Velocity (Vo) = 1,225m/s
Distance travelled (S2) = 76,562m
Time (t2) = 125s
Phase 3
Acceleration (a) = 9.8m/s2
Distance Travelled (St) = S1 + S2 = 98,000m
Time (t3) = 141.4s
Thus total time = t1 + t2 + t3 = 35 + 125 + 141.4 = 301.4s
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