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Sagot :
Answer:
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;
[tex]\underset{F_1}{\rightarrow}[/tex] = 200 × cos(60°)·i + 200 × sin(60°)·j = 100·i + (100·√3)·j
[tex]\underset{F_2}{\rightarrow}[/tex] = 800 × cos(60°)·i - 800 × sin(60°)·j = 400·i - (400·√3)·j
The resultant force, R = [tex]\underset{F_1}{\rightarrow}[/tex] + [tex]\underset{F_2}{\rightarrow}[/tex]
∴ R = 100·i + (100·√3)·j + 400·i - (400·√3)·j = 500·i - (300·√3)·j
Their resultant force magnitude on the sleigh, [tex]\left | R \right |[/tex] = √(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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