The given construction as shown in figure consists of two rhombus with the side ratio 5 : 4. The vertex $A_{2}$ moves in the horizontal direction with a velocity v. Find the velocity of $A_{1}$ .

Question

The given construction as shown in figure consists of two rhombus with the side ratio 5 : 4. The vertex A 2 ​ moves in the horizontal direction with a velocity v. Find the velocity of A 1 ​ .

TestHub · Accepted Answer

With side ratio 5 : 4, y/x = 5/4 at every instant, so $\frac{d y}{d t} = \frac{5}{4} \frac{d x}{d t}$ .

The fixed total length gives $v = \frac{d y}{d t} + \frac{d x}{d t} = \frac{9}{5} \frac{d y}{d t}$ .

Hence the required speed is $\frac{d y}{d t} = \frac{5 v}{9}$ .

Answer: B

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