When a ball bounces, it rises to $\frac{3}{4}$ of the height from which it fell. If the ball is dropped from a height of $32\text{m}$, how high will it rise at the third bounce?

Let the initial height be $H_0=32\text{m}$.
After each bounce, the height becomes $\frac{3}{4}$ of the previous height.

* Height after the 1st bounce ($H_1$):

$$H_1=32\times \frac{3}{4}=24\text{m}$$

* Height after the 2nd bounce ($H_2$):

$$H_2=24\times \frac{3}{4}=18\text{m}$$

* Height after the 3rd bounce ($H_3$):

$$H_3=18\times \frac{3}{4}=\frac{54}{4}=13.5\text{m}$$

The height at the third bounce is $13.5\text{m}$.