Waste less time on Facebook — follow Brilliant.

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 \(0.6 v\)

Note by Akhilesh Prasad
3 years ago

No vote yet
1 vote


Sort by:

Top Newest

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 · 3 years ago

Log in to reply

Thanks a lot. Akhilesh Prasad · 3 years ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...