An asteroid of mass m = 7.5 times 10^12 kg has two rocket thrusters attached to

Question

An asteroid of mass m = 7.5 times 10^12 kg has two rocket thrusters attached to it. One thruster supplies a force with x-and y-components F_1 = (8.0 times 10^7, 7.0 times 10^7) N while the other supplies a force with x- and y-components F_2 = (4.0 times 10^7, -2 times 10^7) N. (You may ignore the mass of the rocket thrusters and their fuel.) (a) (i) what are the x-and y-components of the resultant force acting on the asteroid? (ii) What is the magnitude of the resultant force and in which direction does it act?

Explanation / Answer

part i)

Total x component Fx = F1x + F2x = (8 +4 )e7N = 12e7 N

Total y component Fy = F1y + F2y = 5e7N

part ii)

Resultant force, Fr = sqrt(Fx^2 + Fy^2) = sqrt((12e7)^2 + (5e7)^2) = 13e7 N

let direction be theta angle from x axis

tan(theta) = Fy/Fx

theta = tan-1(Fy/Fx) = tan-1(5/12) = 22.59o

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