Question

Hi,
I need help with a momentum question. Here it is: Your spacecraft is travelling forward with a momentum of 4940 kgm/s. The space station is 40 degrees to the right. The thrusters on the spacecraft exert a force of 1112 N perpendicular to the motion. How many seconds should you turn the thruster on to change your heading to reach the station? I'm comfused and any help would be appreciated. Thanks.

Answer 1

Your spacecraft is travelling forward with a momentum of $4940\frac{kg \cdot m}{s}$ . The space station is $40{}^{\circ}$ to the right. The thrusters on the spacecraft exert a force of $1112N$ perpendicular to the motion. How many seconds should you turn the thruster on to change your heading to reach the station?

Solution.

$\overrightarrow{p_1}$ - an initially momentum of the spacecraft;

$\overrightarrow{p_2}$ - a final momentum of the spacecraft;

$\overrightarrow{\Delta p}$ - changing of the momentum of the spacecraft.

From diagram:

$$\frac {\Delta p}{p _ {1}} = \tan \alpha ;$$ $$\Delta p = p _ {1} \tan \alpha .$$

If a force $F$ is applied to a spacecraft for a time interval $t$ , the momentum of the spacecraft changes by an amount:

$$\Delta p = F t;$$ $$t = \frac {F}{\Delta p};$$ $$t = \frac{F}{p_1 \tan a}.$$ $$t = \frac{1112}{4940 \cdot \tan 40{}^\circ} = 0.27(s).$$

Answer: $t = 0.27s$.