Please show all work and formulas and explain for full points: In the figure, a

Question

Please show all work and formulas and explain for full points:

In the figure, a horse pulls a barge along a canal by means of a rope. The force on the barge from the rope has a magnitude of 7850 N and is at the angle theta = 18 degree from the barges motion, which is in the positive direction of an x axis extending along the canal. The mass of the barge is 9500 kg, and the magnitude of its acceleration is 0.12 m/s2. What are (a) the magnitude and (b) the direction (measured from the positive direction of the x axis) of the force on the barge from the water? Give your answer for (b) in the range of (-180 degree, 180 degree].

Explanation / Answer

a) sum forces in y:

Fy = -7850*sin(18)=-2425.8 N

sum forces in x:

7850*cos(18) + F = 9500*0.12

Fx=-6325.8

mag = sqrt(2425.8^2 + 6325.8^2)=6775 N

b) direction = arctan( 2425.8/6325.8)=-159 degrees

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