Find the magnitude and direction of the resultant of the three force vectors, an

Question

Find the magnitude and direction of the resultant of the three force vectors, and , shown in the figure. These vectors have the following magnitude A=5.0 1b, B=10.0 1b, and c=6.0 1b. Express the direction of the resultant by specifying the angle it makes with the +x-axis, with counterclockwise angles taken to be positive. A player hits a tennis ball into the air with an initial velocity of 36 m/s at 36+ from the vertical. How fast is the ball moving at the highest point in its tracjectory if air resistance is negligible?

Explanation / Answer

here,

writing each force according to their component in respective axis

Fx = Fa + Fb*cos60 = 5 + 10*0.5
Fx = 10 lb

Fy = Fbsin60 - Fc = 10*0.86 - 6
Fy = 2.6 lb

R = sqrt(Fx^2 + Fy^2)

R = sqrt(10^2 + 2.6^2)

R = 10.33 lb

Resultant of three vector is 10.33 lb

TanA = Fy/Fx
A = arcTan(2.6/10)

A = 14.57 degrees

Resultant Vector makes 14.57 degrees with positve X axis

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