Question

NASA is tracking one of its mega space probe as it moves through an astroid belt. They have located the satellite as having position coordinates of -3.00 kilometers in the x-direction and 0 kilometers in the y-direction. Asteroid #1 has a location of 0 kilometers in the x-direction and +1.5 kilometers in the y-direction. Asteroid #2 has a location of 0 kilometers in the x-direction and -1.5 kilometers in the y-direction.

If the mass of the mega space probe is 2.50 x 10⁷ kg and asteroid #1 and #2 both have the same mass of 3.50 x 10¹¹ kg, what is the magnitude of the total force vector of all forces acting on the mega space probe at this instant?

40 to 50 N

30 to 40 N

greater than 70 N

less than 30 N

50 to 60 N

60 to 70 N

Answer 1

F, : 6.624x76 "*2.5X10* 3.5410 astroid-1 1.5m r2 magna mega -space probe 3m Г 1.5m Hia asteroida here Nira = 2 r = r = r² = 32+1.52 = 11.25 km² 11.25X106 m2 r2 force due to Asteroid - l = fil fi GM, M2 .72 here G = 6.674810 nm/ kg? 7 hence 11.25 Xco Fi = 5.191810 51.91N same hence z = F ( because the masses are the magnitude of forces due to both asteroids same) will be

but the direction of forces is different Acc. to geometry (trigonometry) o cara tamo = 2 o= tan-(0.5) = 26.56 hence the magnitude of the Resultang force will be Fresultant 2F, coso 2 f, COS(26.55) : 2x 51.91x cos(26.58) Free 92.86N hence the right answere is greater than ton
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