Three particles A, B and C of equal mass move with equal speed V along the medians of an equilateral triangle as shown in hgure. They collide at the centroid G of the triangle. After the collision, A comes to test, B retraces its path with the speed V. What is the velocity of C ?

Options

A. `v` along `BG`
B. `(v)/(2)` along `GB`
C. Zero
D. `v` along `CG`

Answer

A

Explanation

Along X-axis :
`0+mv cos theta - mv cos theta = 0- mv cos theta + mv_(x)`
`v_(x) = v cos theta(theta = 30^@)`
Along Y-axis :
`-mv + mv sin theta + mv sin theta = 0 - mv sin theta + mv_(y)`
`v_(y) = v sin theta(theta = 30^@) , v_("net") = sqrt(v_(x)^(2) + v_(y)^(2))`.