# Linear Algebra

Two prospectors are pulling on ropes attached around the neck of a donkey that doesn’t want to move. One
prospector pulls with a force of 25 lbs, and the other pulls with a force of 50 pounds. If the angle between the
ropes is 30 degrees, then how much force must the donkey use in order to stay put? (The donkey knows the
proper direction in which to apply his force.)

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1. Assuming the forces are acting 12.5 degrees (25/2) out from the head of the donkey in either direction then the forward force would be 55 * cos12.5 + 75 * cos12.5 = 127 N to 3 s.f. so the donkey pulls backwards with 127 N - but this depends entirely on the orientation of the diagram of forces, if there is one

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2. Since the system is in Equilibrium, the
force of the donkey must be equal and opposite the applied force:

Fd = -(25 + 50[30o]) = -(25 + 43.3+25i) = -(68.3 + 25i) = -68.3 - 25i = 72.7 Lbs[20.1o] S. of W.

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