A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision between ball and floor is 0.5, after hitting the floor, the ball rebounds to a height of ______ m.

A ball is dropped from height $$h = 20$$ m. Coefficient of restitution $$e = 0.5$$.

Velocity just before hitting the floor.

Using $$v^2 = u^2 + 2gh$$ with $$u = 0$$:

$$

v_{\text{before}} = \sqrt{2gh} = \sqrt{2 \times 10 \times 20} = 20 \text{ m/s}

$$

Velocity just after rebound.

By definition of coefficient of restitution:

$$

v_{\text{after}} = e \times v_{\text{before}} = 0.5 \times 20 = 10 \text{ m/s}

$$

Maximum rebound height.

Using $$v^2 = u^2 - 2gH$$ with $$v = 0$$:

$$

H = \frac{v_{\text{after}}^2}{2g} = \frac{100}{20} = 5 \text{ m}

$$

Alternatively: $$H = e^2 \times h = (0.5)^2 \times 20 = 0.25 \times 20 = 5$$ m.

The answer is $$\boxed{5}$$ m.