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 14.1 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 meaure 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 0.763 kg, how much work is done by the drag force on the rocket during its ascent? (46.1 is incorrect) Keep in mind that the drag force should act to oppose the motion of the rocket. *Please make sure answer is correct as I paid $3 for this question. Thanks!

Explanation / Answer

Let’s determine the work that is done by the thrust force.
Work = 14.1 * 14.6 = 205.86 N * m
This is the rocket’s maximum kinetic energy.

KE = ½ * 0.763 * v^2 = 205.86
v = (205.86 ÷ 0.3815) = 785.3559

This is approximately 28 m/s. As the rocket rises to its maximum height, its velocity decreases to 0 m/s. Let’s use the following equation to determine this distance.

vf^2 = vi^2 + 2 * a * d, vf = 0, a = -9.8 m/s^2
0 = 205.86 + 2 * -9.8 * d
19.6 * d = 205.86
d = 205.86 ÷ 19.6
This is approximately 10.5 meters.

Total height = 14.6 + (205.86 ÷ 19.6)
This is approximately 25.1 meters. The drag force caused the rocket’s maximum height to decrease from 25.1 meters to 19.1 meters.

Work = 0.763 * 9.8 * (19.1 – 25.1) = -44.8644 joules

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