Answer to Question #141316 in Physics for Sydney

Question

A 3250 kg rocket is traveling through space at 6.70 m/s. Thrusters are fired for 3.10 seconds. This causes the rocket to increase its velocity to 10.5 m/s. Calculate the average force needed to cause this increase.

Answer 1

We can find the average force needed to cause the increase of rocket's velocity from the

impulse-momentum change equation:

$$F_{avg}\Delta t=m\Delta v,$$ $$F_{avg}\Delta t=m(v_f-v_i),$$

here, $F_{avg}$ is the average force needed to cause the increase of rocket's velocity,

$\Delta t=3.10\ s$ is time during which the thrusters are fired, $m=3250\ kg$ is the mass of the rocket, $v_i=6.70\ \dfrac{m}{s}$ is the initial velocity of the rocket, $v_f=10.5\ \dfrac{m}{s}$ is the final velocity

of the rocket.

Then, from this equation we can calculate $F_{avg}$:

$$F_{avg}=\dfrac{m(v_f-v_i)}{\Delta t},$$ $$F_{avg}=\dfrac{3250\ kg\cdot(10.5\ \dfrac{m}{s}-6.70\ \dfrac{m}{s})}{3.10\ s}=3984\ N.$$

Answer:

$F_{avg}=3984\ N.$