Two reindeer-in-training pull on a sleigh. Connie pulls with a force of 200 Nat an angle of 60 degrees above the x-axis, while Randolph pulls with a

force of 800 N at an angle of 60 degrees below the x-axis. What is their

resultant force on the sleigh?

Their resultant force magnitude on the sleigh is approximately 583.095 N

Explanation:

The given parameters are;

The magnitude and direction in which the two reindeer-in-training pull on the sleigh are;

The force with which Connie pulls on the sleigh, F₁ = 200 N

The direction in which Connie pulls on the sleigh = 60° above the x-axis

The force with which Randolph pulls on the sleigh, F₂ = 800 N

The direction in which Connie pulls on the sleigh = 60° below the x-axis

The vector form of the force with which the two reindeer-in-training pulls the sleigh is given as follows;

= 200 × cos(60°)·i + 200 × sin(60°)·j = 100·i + (100·√3)·j

= 800 × cos(60°)·i - 800 × sin(60°)·j = 400·i - (400·√3)·j

The resultant force, R = +

∴ R = 100·i + (100·√3)·j + 400·i - (400·√3)·j = 500·i - (300·√3)·j

Their resultant force magnitude on the sleigh, = √(500² + (-300)²) ≈ 583.095 N

The direction of the resultant force = arctan(-300/500) = arctan(-0.6) ≈ -30.964 which is approximately 30.964° below the x-axis.

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