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Standard X

Physics

Conservation of Momentum

A rocket moto...

Question

A rocket motor consumes $100 K g$ of fuel per second, exhausting it with a speed of $5 \times 10^{3} m s^{- 1}$ . (i) What force is exerted on the rocket? (ii) What will be the velocity of the rocket at the instant its mass is reduced ( $1 / 20$ )th of its initial mass, its initial velocity being zero. Neglect gravity.

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Solution

It is given that

$m = 100 K g$

$v = 5 \times 10^{3} m / s$

(1) $F = m a$

$= m \frac{v}{t}$

$= v \frac{m}{t}$

$= 5 \times 10^{3} \times 100$

$= 5 \times 10^{5} K g m / s^{- 2}$

(2) when mass is reduced, then

$m^{'} = 5 k g$

$F = m a$

$5 \times 10^{5} = 5 \times a$

$a = 10^{5}$

$\frac{v}{t} = 10^{5}$

$v = 10^{5} m / s$

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A rocket motor consumes 100 Kg of fuel per second, exhausting it with a speed of 5×103 ms−1. (i) What force is exerted on the rocket? (ii) What will be the velocity of the rocket at the instant its mass is reduced (1/20)th of its initial mass, its initial velocity being zero. Neglect gravity.

It is given that m=100Kg v=5×103m/s (1) F=ma =mvt =vmt =5×103×100 =5×105Kgm/s−2 (2) when mass is reduced, then m′=5kg F=ma 5×105=5×a a=105 vt=105 v=105m/s