Question

A toy rocket is launched vertically from ground level (y = 0.00 m),
at time t = 0.00 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 72 m and acquired a velocity of 30 m/s. The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground with negligible air resistance. The speed of the rocket upon impact on the ground is closest to ...?
Show Step by step please.

Answer 1

i worked on this problem and found 56.67 m/s am I correct?

Answer 2

\[y(t) = -9.8t^{2}+30t+72\]
this is the equation to be used where t = 0 is the time that the rocket stopped burning.

to find the time when it hits, you can set y(t) = 0 and solve for t.

you should get a positive and a negative. only the positive value is valid.

substitute that into the velocity equation, which should be like this (again, t is time after the rocket stopped burning)

\[v(t) = 2(-9.8)t+30\]

Answer 3

i got a different velocity.

Answer 4

what did you get?

Answer 5

compute!

Answer 6

what did you get for time?