Help! An asteroid is heading towards us at 14 km/s . Scientists decide the best

Question

Help! An asteroid is heading towards us at 14 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 19 km/s and its new trajectory will be at an angle of 25 to its original path. n 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.

Explanation / Answer

Initial velocity = ux =14km/s = 14000 m/s

Final velocity in the initial direction, vx = 19cos25 = 19000cos25 m/s

t = 8 min = 8 x 60 = 480 s

so, ay = [vx-ux]/t = [19000cos25 - 14000]/480 = 6.7 m/s2.

This is the acceleration of the asteroid in the initial direction.

Acceleration in the transverse direction will be:

ay = [19000sin25]/480 = 16.73 m/s2.

so, a = <6.7 , 17> m/s2.

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