A ball is projected from a point on a smooth horizontal floor at an angle `theta ` with the horizontal . Speed of projection is u . Ball collides with the floor several times . Find the total time and horizontal distance covered by the ball .

Explanation

To solve the problem of a ball projected at an angle \(\theta\) with an initial speed \(u\) on a smooth horizontal floor, we need to find the total time of flight and the total horizontal distance covered by the ball after several collisions with the floor.

### Step 1: Determine the time of flight for the first projectile motion
The time of flight for the first projectile motion can be calculated using the formula:
\[ T_1 = \frac{2u \sin \theta}{g} \]
where \(g\) is the acceleration due to gravity.
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