If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is -- [2008]

Question

A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from $60 °$ to $30 °$ at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic ( $g = 10 {m/s}^{2}$ ). [2008]

Q. If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is --

Smart Achievers · Accepted Answer

(3)

The velocity of the block along BC just before collision is $v \cos 30 °$ . The impact forces act perpendicular to the surface so the component of velocity along the incline remains unchanged.

Also, since the collision is elastic, the vertical component of velocity $(v \sin 30 °)$ before collision changes in direction, the magnitude remaining the same as shown in the figure. So the rectangular components of velocity after collision are as shown in the figure. This means that the final velocity of the block should be horizontal making an angle $30 °$ with BC. Therefore the vertical component of the final velocity of the block is zero.

Solution

1 $\sqrt{30} m/s$

2 $\sqrt{15} m/s$

3 $0$

4 $- \sqrt{15} m/s$

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Solution

1 30 m/s

2 15 m/s

3 0

4 -15 m/s

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1 $\sqrt{30} m/s$

2 $\sqrt{15} m/s$

3 $0$

4 $- \sqrt{15} m/s$