Question

A hemisphere 'S' and a particle 'P' are of same mass 'm'. P is dropped from

a height 'h'. A hemisphere 'S' is kept on a smooth horizontal surface. The particle 'P' collides elastically with hemisphere at the point shown in the figure. If theta = 45 deg and after collision the velocity of the particle becomes horizontal. Find the velocities of hemisphere 'S' and particle 'P' after collision.

Answer 1

The hemisphere 'S' will move at a 45-degree angle upwards with the same velocity magnitude as 'P' moves horizontally post-collision.

Step-by-step explanation:

After an elastic collision of two objects with equal mass where one was initially at rest and the other had a horizontal velocity post-collision, both objects will have identical magnitudes of velocity but in perpendicular directions. As the collision is elastic, momentum conservation applies in both the horizontal and vertical directions. Given the symmetry and the 45-degree approach angle, the final velocities can be deduced from the geometry of the collision. Therefore, the final velocity of 'S' will be at a 45-degree angle upwards and to the opposite side of 'P's incoming direction, with the same magnitude as 'P's final horizontal velocity.