Question

a hinged construction consists of three rhombus with the ratio of sides (5:3:2). vertex A3 moves in the horizontal direction with velocity V . velocity of A2 will be?

Answer 1

Hope, your question is as shown in figure.

Final Answer : 0.8V

Steps:
1) We know,
Diagonal of rhombus is proportional to its side.
=> Cor-responding ratio of diagonals = 5:3:2
Let them be 5y, 3y,& 2y respectively as shown in figure.

2) Now,
$V_{A_3}-V_{A_o} = \frac{d(A_oA_3)}{dt}\\ => V-0 = \frac{d(10y)}{dt}\\ => V-0 = 10\frac{dy}{dt} --(1)$

3)Also,
$V_{A_3}-V_{A_2} = \frac{d(A_3A_2)}{dt} \\ => V-V_{A_2} = \frac{d(2y)}{dt} \\ => V-V_{A_2} =2 \frac{d(y)}{dt}-(2)$

Elimination $\frac{dy}{dt}$ from above equations,
we get
$\boxed{V_ {A_2} = 0.8 V }$

Hence, Velocity at $A_2$ is $0.8 V$ .