Robert has just bought a new model rocket, and is trying to measure its flight c

Question

Robert has just bought a new model rocket, and is trying to measure its flight characteristics. The rocket engine package claims that it will maintain a constant thrust of 11.1 N until the engine is used up. Robert launches the rocket on a windless day, so that it travels straight up, and uses his laser range-finder to measure that the height of the rocket when the engine cuts off is 14.6 m. He also measures the rocket's peak height, which is 19.1 m. If the rocket has a mass of 0.713 kg, how much energy is dissipated by the drag force on the rocket during its ascent? (Even though this is energy lost, give your answer as a positive value.)

Explanation / Answer

Solution:

The engine is cut of at h = 14.6 m height

Total energy of the rocket at the height h =mgh  + 1/2 mv2

The maximum height = H =19.1 m

The only energy at the highest point = potential = mgH

from energy conservation, mgH = mgh  + 1/2 mv2

=> 1/2 mv2 = mg(H-h)

=> v = sqrt (2g(H-h) = sqrt (2*9.8(19.1-14.6)] = 9.4 m/s

work done due to the thrust = F h = (11.1)(14.6) = 162.06 Nm

Energy at that height = mgh+1/2mv2= gH = (0.713)(9.81)(19.1) = 133.59 Nm

Energy dissipated = 162.06 - 133.59 = 28.5 J

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