Question

when a rocket that weighs 2400 n on earth is fired the force of propulsion is 4000 n. find the acceleration of the rocket. (g = 9.8 m/s²) (write your answer in 3 significant figures)

Explanation:

Step1: Calculate the mass of the rocket

We know that weight \(W = mg\). Given \(W = 2400\ N\) and \(g=9.8\ m/s^{2}\). Then \(m=\frac{W}{g}\).

$$m=\frac{2400}{9.8}\ kg\approx244.9\ kg$$

Step2: Apply Newton's second law \(F_{net}=ma\)

The net force \(F_{net}=F - W\), where \(F = 4000\ N\) and \(W = 2400\ N\). So \(F_{net}=4000 - 2400=1600\ N\)
Since \(F_{net}=ma\), then \(a=\frac{F_{net}}{m}\)
Substitute \(m = \frac{2400}{9.8}\ kg\) and \(F_{net}=1600\ N\) into the formula:

$$a=\frac{1600}{\frac{2400}{9.8}}=\frac{1600\times9.8}{2400}$$

$$a=\frac{15680}{2400}\approx6.53\ m/s^{2}$$

Answer:

\(6.53\ m/s^{2}\)