Three astronauts, propelled by jet backpacks, push and guide a 121 kg asteroid t

Question

Three astronauts, propelled by jet backpacks, push and guide a 121 kg asteroid toward a processing dock, exerting the forces shown in the figure, with F1 = 27 N, F2 = 59 N, F3 = 36 N, 1 = 30°, and 3 = 60°. What is the (a) magnitude and (b) angle (measured relative to the positive direction of the x axis in the range of (-180°, 180°]) of the asteroid's acceleration?

Three astronauts, propelled by jet backpacks, push and guide a 121 kg asteroid toward a processing dock, exerting the forces shown in the figure, with Fi 27 N, F2 59 N, Fa 36 N e1 30 and e3 60°. What is the (a) magnitude and (b) angle (measured relative to the positive direction of thexaxis in the range of (-1800, 180 1) of the asteroid's acceleration?

Explanation / Answer

F1 = 27N , F2 = 59 N , F3 = 36 N

1 = 30°, and 3 = 60°.

F1 = 27cos(30)i +27sin(30)j

F1 = 23.38 i + 13.5 j

F2 = 59 i

F3 =36cos(60) i - 36sin(60)j

F3 = 18i - 31.2 j

net force =F =ma

F1 +F2+F3 = ma

23.38i+13.5j +59i +18i-31.2j = 121*a

a = 0.83i -0.146 j

(A) magnitude a = (0.83^2+0.146^2)^0.5

a = 0.843 m/s^2

(b) direction theta = arctan(0.146/0.83)

theta = - 9.97 degrees

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