A ball is dropped from a height of 16 m on a horizontal floor. If it rebounds to a height of 9 m after striking the floor, the coefficient of restitution between ball and floor is A. $$\frac{1}{4}$$ B. $$\frac{2}{3}$$ C. $$\frac{3}{4}$$ D. $$\frac{4}{3}$$

$$ rac{1}{4}$$
$$ rac{2}{3}$$
$$ rac{3}{4}$$
$$ rac{4}{3}$$

The correct answer is $\boxed{\frac{2}{3}}$.

The coefficient of restitution is a measure of how much energy is lost when two objects collide. It is defined as the ratio of the relative speed of the objects after the collision to the relative speed of the objects before the collision.

In this case, the ball is dropped from a height of 16 m and rebounds to a height of 9 m. This means that the relative speed of the ball after the collision is 16 m/s – 9 m/s = 7 m/s. The relative speed of the ball before the collision is the speed of the ball as it falls, which is 16 m/s. Therefore, the coefficient of restitution is $\frac{7 m/s}{16 m/s} = \frac{2}{3}$.

Option A is incorrect because the coefficient of restitution cannot be less than 0. This is because the relative speed of the objects after the collision cannot be negative.

Option B is incorrect because the coefficient of restitution cannot be greater than 1. This is because the relative speed of the objects after the collision cannot be greater than the relative speed of the objects before the collision.

Option C is incorrect because the coefficient of restitution cannot be equal to 1. This is because the ball loses some energy when it collides with the floor.