Question

A friend is writing a science fiction screenplay about an asteroid on a collision course with Earth. She asks you to calculate some numbers so her scenario will be correct. Astronauts will attach a rocket engine to the asteroid in an attempt to divert it. The asteroid is moving at 21 km/s. The rocket will provide an acceleration of 0.035 km/s2 at a right angle to the original motion. The rocket only has enough fuel to provide this acceleration for 40 seconds. Will this change the direction of the asteroid’s motion by at least 22°, enough to miss Earth and save civilization? (15 pts, according to Grading for problem solving, see reverse side. Your group should submit one analysis, with all group member’s names, either on the Problem solving framework or the plain white paper provided.)

Answer 1

Answer:

No, the deviation in the path of asteroid is not by 22°

Explanation:

Given:

velocity of asteroid, $v_a=21\ km.s^{-1}$

acceleration of the rocket, $a=0.035\ km.s^{-2}$

time of acceleration, $t=40\ s$

Now, the final velocity of the asteroid:

using the equation of motion,

$v=u+a.t$

where:

$v=$ final velocity

$u=$ initial velocity in the direction

$v=0+0.035\times 40$

$v=1.4\ km.s^{-1}$

Now direction of the resultant velocity:

$\tan\beta=\frac{v_a}{v}$

$\tan\beta=\frac{21}{1.4}$

$\beta=86.186^{\circ}$

So, the deviation in the asteroid:

$\theta=90-\beta$

$\theta=90-86.186$

$\theta=3.814^{\circ}$