There are a few reasons why a ball bounces higher on a hard surface compared to a soft surface:

1. Conservation of energy: When a ball hits a hard, rigid surface, more of the ball’s kinetic energy is conserved and converted back into upward motion. On a soft surface, some of the ball’s kinetic energy gets absorbed and converted into deformation of the surface, reducing the rebound.

2. Coefficient of restitution: The coefficient of restitution is a measure of how much energy is lost in the collision. Hard surfaces have a higher coefficient of restitution, meaning more of the ball’s energy is returned to the ball on impact, allowing it to bounce higher.

3. Impulse: The change in momentum during the collision is greater on a hard surface. This larger impulse provides a stronger upward force to propel the ball back into the air.

4. Deformation: On a soft surface, the ball deforms more on impact, absorbing some of its kinetic energy. On a hard surface, the deformation is less, allowing more of the energy to be converted into the upward bounce.

So in summary, the key factors are the conservation of energy, the coefficient of restitution, the impulse experienced, and the reduced deformation – all of which contribute to a higher bounce on a hard surface compared to a softer one.