Two drunken college students have filled an empty beer keg w

Two drunken college students have filled an empty beer keg with rocks and tied ropes to it in order to drag it down the street in the middle of the night. The stronger of the two students pulls with a force of 100 pounds at a heading of N77E and the other pulls at a heading of S68E. What force should the weaker student apply to his rope so that the keg of rocks heads due east? What resultant force is applied to the keg? Round your answer to the nearest pound.

Solution

The stronger students pulls with a force of 100 pounds at heading of N77E:

Fx = 100sin77

Fy = 100cos77

Weaket student pulls it with force F at heading S68E

Fx = Fsin68

Fy = Fcos68

Now force along y direction is balanced:

Fcos68 = 100cos77

F =60.05 = 60 pounds force