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 all the steps please..

Answer 1

as shown in figure rocket starts at B with velocity 32m/s.When it reaches maximum height it comes to a stop before coming to ground.During this flight from B to C and back to A ,only acceleration acting on it is acceleration due to gravity.Which is positive coming downward and negative going upward.
for (2)
\[v ^{2}-u ^{2}=2gh\]
\[0^{0}-(30)^{2}=2*-9.8*h,h=\frac{ 900 }{17.6 }\]
for (3)
Total distance h=72+900/17.6
u=0m/s
g=9.8m/s^2
v=?
\[use v ^{2}-u ^{2}=2gh\]

Answer 2

\[v ^{2}-0^{2}=2*9.8*\left( 72+\frac{ 900 }{17.6 } \right)\]
\[v ^{2}=17.6*72+900=9\left( 17.6*8+100 \right)=9\left( 140.8+100 \right)=9*240.8=2167.2\]
\[v=\sqrt{2167.2}m/s\]

Answer 3

correction
in figure(1) at (2) write 30m/s in place of 32m/s.

Answer 4

as shown in figure rocket starts at B with velocity 32m/s.When it reaches maximum height it comes to a stop before coming to ground.During this flight from B to C and back to A ,only acceleration acting on it is acceleration due to gravity.Which is positive coming downward and negative going upward.
for (2)
\[v ^{2}-u ^{2}=2gh\]
\[0^{0}-(30)^{2}=2*-9.8*h,h=\frac{ 900 }{17.6 }\]
for (3)
Total distance h=72+900/17.6
u=0m/s
g=9.8m/s^2
v=?
\[use v ^{2}-u ^{2}=2gh\]