You\'re heading an international effort to save Earth from an asteroid heading t

Question

You're heading an international effort to save Earth from an asteroid heading toward us at 15.0 km/s. Your team mounts a rocket on the asteroid and fires it for exactly 10 min, after which theta steroid is moving at 19.0 km/s at 24 degree to its original path. Assume that the positive x axis is in the direction of the initial motion of asteroid and y axis is perpendicular to it. In a news conference, what do you report for the acceleration imparted to the asteroid? Express your answers using three significant figures separated by a comma. a_x, a_y = __________ m/s^2

Explanation / Answer

v0x = 15 km/s , v0y = 0

vfx = 19 cos24 = 17.4 km/s

vfy = 19 sin24 = 7.73 km/s

acceleration = change in velocity / time

a_x = (vfx - v0x) / t

= (17.4- 15) / (10 x 60)

= 3.93 x 10^-3 km/s^2

= 3.93 m/s^2

a_y = (7.73 - 0) / 600

= 0.0129 km/s^2

= 12.9 m/s^2

Ans: (3.93 , 12.9)

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