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 12.3 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 10.2 m. He also measures the rocket\'s peak height, which is 14.7 m. If the rocket has a mass of 0.613 kg, how much work is done by the drag force on the rocket during its ascent?

Answer 1

Assuming no drag, the speed of rocket is given by -

v = (2T / m) H

where, H = height of the rocket when an engine cuts off = 10.2 m

T = constant thrust = 12.3 N

m = mass of the rocket = 0.613 kg

then, we get

v = [2 (12.3 N) / (0.613 kg)] (10.2 m)

v = 409.3 m²/s²

v = 20.2 m/s

Now, using conservation of energy and we have -

K.E = U (1/2) m v₀² = m g h

v₀² = 2 g h

v₀ = 2 (9.8 m/s²) [(14.7 m) - (10.2 m)]

v₀ = 9.391 m/s

How much work is done by the drag force on rocket during its ascent?

we know that,   W = KE

W = (1/2) m (v² - v₀²)

W = (0.5) (0.613 kg) [(409.3 m²/s²) - (88.2 m²/s²)]

W = 98.4 J