College Physics Problem. Please show all work. Two teenagers are pulling on rope

Question

College Physics Problem. Please show all work.

Two teenagers are pulling on ropes attached to a tree. The angle between the ropes is 32.2 degree. David pulls with a force of 418.0 N and Stephanie pulls with a force of 318.0 N. (Assume David pulls in the +x-direction and Stephanie pulls in the +x- and +y-directions.) (a) Find the component form of the net force (in N). (Express your answer in vector form.) F_net = 1671.7 i + 222.7 j N (b) Find the magnitude of the resultant (net) force (in N) on the tree and the angle it makes with David's rope (in degrees counterclockwise from the +x-axis). magnitude 707.66 N direction 71.66 degree counterclockwise from the +x-axis

Explanation / Answer

F_D = 418 i

F_S = 318(cos32.2i + sin32.2j)

F_S = 269i + 169.5 j

(A) Fnet = F_D + F_S

Fnet = 687 i + 169.5 j N

Ans: (687 N , 169.5 N)

(b) magnitude = sqrt(687^2 + 169.5^2) = 708 N

direction angle = tan^-1(169.5 / 687) = 14 deg

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