Two forces and are used to pull a car, which met an accident. The angle between the two forces is . Find the value of for which the resultant force is equal to .

Explanation: Step 1: Understand the formula for the resultant of two forces According to the parallelogram law of vector addition, the magnitude of the resultant force of two forces and acting at an angle to each other is given by: Step 2: Substitute the given condition The problem states that the resultant force is equal to . Therefore, we equate to this value: Step 3: Square both sides to solve for Squaring both sides eliminates the square roots: Subtract from both sides: Since the forces and are non-zero pulling forces, their product . Thus, we must have: Step 4: Determine the angle We know that the cosine of an angle is zero when the angle is : Therefore, the angle between the two forces must be . Correct Answer: C)

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NIMCET 2020 — Mathematics PYQ

NIMCET | Mathematics | 2020

Two forces $F_{1}$ and $F_{2}$ are used to pull a car, which met an accident. The angle between the two forces is $θ$ . Find the value of $θ$ for which the resultant force is equal to $F_{1}^{2} + F_{2}^{2}$ .

NIMCET 2020 — Mathematics PYQ

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