Strange moving Rhombus

The given construction as shown in figure consists of two rhombus with the ratio $3 : 2$ . the vertex $A_2$ moves in the horizontal direction with a velocity $v$ . Find the velocity of $A_1$ .

Help me with this one

The answer is $0.6 v$

#Mechanics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Let's take this with a specific example. Scene 1. Both rhombuses are squares. Hence, A1 will be at a distance of 3√2 from A0 and A2 will be at a distance of (3+2)√2 from A0 The distances are calculated using basic trigonometry.

Scene 2. Both A2 and A1 have moved forward. Hence, let's assume the new angle formed at A0 is 60 degree. Because opposite angles are equal in a rhombus, all angles on that imaginary horizontal line are also 60 deg. Using trigonometry again, we calculate the distance of A2 as 5√3 and that of A1 as 3√3

In the same time, A2 has moved a distance of 5(√3-√2) and A1 has moved 3(√3-√2). Since the time is same, proportion of speed = proportion of distance. Hence 3/5=0.6

Aditya Mani - 6 years, 11 months ago

Thanks a lot.

Akhilesh Prasad - 6 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$