Please answer asap A block of mass 3.2 kg is initially at rest on a wedge of mas

Question

Please answer asap

A block of mass 3.2 kg is initially at rest on a wedge of mass 25 kg, height 0.30 m, and an incline angle Theta = 35 degree as shown in the figure below. There is no friction between the wedge and the floor. Starting at the top of the incline, the block is released and slides toward the bottom of the wedge. At the same time, the wedge "recoils" and slides some distance L to the right. Find L when the block has reached the bottom of the wedge. Hint: The center of mass of a right triangle of height h is a distance h/3 above the base of the triangle. (For simplicity, you may treat the block as a point mass.) L = cm

Explanation / Answer

there is no external force in horizontal direction,

so centre of mass will not move in horizontal .

base width d = 0.30 /tan35 = 0.428 m

block will move ( L - d) in horizontal and wedge L distance.

3.2 x (L - 0.428) + 25 x L = 0

L = 0.0486 m   = 4.86 cm

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