Physics help??????????, have the answer, but don't know how it was found?

Question

A small 523 g model rocket lifts off the ground, accelerating quickly. 4.2 s later the engine cuts out at a height of 845 m, at which time the rocket is travelling at 152 m/s. What power was demonstrated by the engine? (Assume little mass change of the rocket during the flight

Answer: 2.5x103 W (Rocket has gained both kinetic and potential energy.)

i tried this can't seem to get it

Answer 1

This can be done as an energy calculation.  The gravitational potential energy at brennschluss is 0.523 x 9.8 x 845 joules, and the kinetic energy is 0.5 x 0.523 x (152)^2 joules.  Add these for the total energy, and divide by 4.2 seconds to get watts.  My calculation gives 2469.68 watts.

Answer 2

Gain in potential energy by the rocket:

ΔPE = mgh = 0.523x9.8x845 = 4,331 J

Gain in kinetic energy:

ΔKE = (1/2)mv² = 0.5x0.523x152² = 6,042 J

Total mechanic energy gained:

ΔE = ΔPE + ΔKE = 4,331 + 6,042 = 10,373 J

Power of the engine:

P = W/t = ΔE/t

P = 10,373 / 4.2 =  2,470 watt or 2.47 kW

Note: Remember that mass is measured in kilogram. (m = 523 g = 0.523 kg)