The toy rocket is launched vertically from ground level, 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 total energy of the rocket, which is a sum of its kinetic energy and potential energy, is constant.
At a height of 72 m with the rocket moving at 30 m/s, the total energy is m*9.8*72 + (1/2)*m*30^2 where m is the mass of the rocket.
At ground level, the total energy is 0*m*9.8 + (1/2)*m*v^2.
Equating the two gives: m*9.8*72 + (1/2)*m*30^2 = 0*m*9.8 + (1/2)*m*v^2
=> 9.8*72 + (1/2)*30^2 = (1/2)*v^2
=> v^2 = 11556/5
=> v = 48.07
The velocity of the rocket when it impacts the ground is 48.07 m/s