Question

An asteroid is heading towards us at 11 km/s . Scientists decide the best solution is to attach a rocket to the asteroid and fire it to change the trajectory of the asteroid. If the rocket is fired for 8 min, the scientists calculate that the new speed for the asteroid will be 20 km/s and its new trajectory will be at an angle of 29 degrees to its original path. In the process described above, what is the acceleration of the asteroid?
Express your answers using two significant figures separated by a comma. Assume that the positive x axis is in the direction of the initial motion of the asteroid. The final motion of the asteroid has components in the x and positive y directions only.

Answer 1

Answer:

$a = (0.013 \hat i + 0.02\hat j)km/s^2$

Explanation:

As we know that acceleration is defined as rate of change in velocity

So we can say

$v_i = 11 km/s$

$v_f = 20 km/s(cos29\hat i + sin29\hat j)$

now we will have

$v_f = 20 km/s(0.87\hat i + 0.48\hat j)$

now this took total time of

$t = 8 min = 480 s$

now we have

$a = \frac{v_f - v_i}{t}$

$a = \frac{17.4\hat i + 9.6\hat j - 11\hat i}{480}$

$a = (0.013 \hat i + 0.02\hat j)km/s^2$