At a picnic, there is a contest in which hoses are used to shoot water at a beac

Question

At a picnic, there is a contest in which hoses are used to shoot water at a beach ball from three directions. As a result, three forces act on the ball, Upper F Subscript 1 Baseline Overscript right-arrow EndScripts, Upper F Subscript 2 Baseline Overscript right-arrow EndScripts, and Upper F Subscript 3 Baseline Overscript right-arrow EndScripts (see the drawing). The magnitudes of Upper F Subscript 1 Baseline Overscript right-arrow EndScripts and Upper F Subscript 2 Baseline Overscript right-arrow EndScripts are F1 = 89.0 newtons (N) and F2 = 98.0 N. Determine (a) the magnitude of Upper F Subscript 3 Baseline Overscript right-arrow EndScripts and (b) the angle such that the resultant force acting on the ball is zero.

Explanation / Answer

F1 = 89cos60i - 89sin60 j

F2 = -98 i

F3 = F3xi + F3yj

Fnet = 0

F1 + F2 + F3 = 0

89*cos60i - 89*sin60 j - 98i + F3xi + F3yj = 0i + 0 j

89*cos60 - 98 + F3x = 0

F3x = -53.5 N

-89*sin60 + F3y = 0

F3y = 77.1 N

F3 = sqrt(53.5^2 + 77.1^2) = 93.8 N

theta = tan^-1(F3y/F3x) = 55.24 degrees

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