An unfueled 1 000-kg experimental rocket sled on level frictionless rails is loaded with 50 kg of propellant. It exhausts the propellant in a 20 s "burn." If the rocket, initially at rest, moves at 160 m/s after the burn, what impulse is experienced by the rocket sled?Select one:a.1.9 × 105 kg·m/sb.1.6 × 105 kg·m/sc.1.5 × 105 kg·m/sd.1.1 × 105 kg·m/s
Question
An unfueled 1 000-kg experimental rocket sled on level frictionless rails is loaded with 50 kg of propellant. It exhausts the propellant in a 20 s "burn." If the rocket, initially at rest, moves at 160 m/s after the burn, what impulse is experienced by the rocket sled?Select one:a.1.9 × 105 kg·m/sb.1.6 × 105 kg·m/sc.1.5 × 105 kg·m/sd.1.1 × 105 kg·m/s
Solution
Impulse is defined as the change in momentum of an object when a force is applied. Momentum is mass times velocity.
The initial momentum (P_initial) of the rocket sled is 0, because it is initially at rest (so its velocity is 0).
The final momentum (P_final) of the rocket sled is its final velocity times its final mass. The final velocity is given as 160 m/s. The final mass is the initial mass of the sled (1000 kg) minus the mass of the propellant that was used (50 kg), so the final mass is 950 kg.
So, P_final = (950 kg)(160 m/s) = 152000 kg·m/s.
The impulse experienced by the rocket sled is the change in momentum, which is P_final - P_initial = 152000 kg·m/s - 0 = 152000 kg·m/s.
So, the correct answer is closest to 1.5 × 10^5 kg·m/s. Therefore, the answer is (c) 1.5 × 10^5 kg·m/s.
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