A rocket of instantaneous mass 100 kg ejects fuel backward at a rate 4 kg/s with relative exhaust speed 500 m/s. Neglect gravity. If its instantaneous acceleration is N m/s², find N.
Physics · Center of maas , Momentum and Collision · variable mass system
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Question

A rocket of instantaneous mass 100 kg ejects fuel backward at a rate 4 kg/s with relative exhaust speed 500 m/s. Neglect gravity. If its instantaneous acceleration is N m/s², find N.

G1 Physics · Accepted Answer

The thrust magnitude of a rocket is F(thrust) = u |dM/dt|. Here, u = 500 m/s, |dM/dt| = 4 kg/s. Therefore F(thrust) = 500×4 = 2000 N. At the instant when rocket mass is 100 kg: a = F/M = 2000/100 = 20 m/s². Hence N = 20.