Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown. The velocity of A to the right is 10 m s⁻¹. What is the speed of B when α = 60°?

Question

G1 Physics · Accepted Answer

Step 1: Let OA=x and OB=y. Because the rod length is fixed, x²+y²=L². Step 2: Differentiate: x(dx/dt)+y(dy/dt)=0. Step 3: The speed of A is |dx/dt|=10 m s⁻¹. At the instant shown, tanα=y/x, so x/y=cot60°=1/√3. Step 4: Therefore the magnitude of B's speed is |dy/dt|=(x/y)|dx/dt|=10/√3≈5.8 m s⁻¹. Final answer: C. Note: the printed solution on the supplied page gives D, but the rigid-rod constraint gives C.