A completely elastic ball is dropped from a height of 10, $9 \mathrm{~m}$ onto an equally completely elastic slope, which has an inclination of $30^{\circ}$. How high and how far will the ball bounce back?
A test falls from a height $s$ onto a slope; its final velocity is $v=\sqrt{2 g s}$; with this velocity, the body will bounce back at an angle of $\alpha=30^{\circ}$ to the horizontal plane. The height of its ascent is:

$$
h=\frac{v^{2} \sin ^{2} \alpha}{2 g}=s \sin ^{2} \alpha=2.725 \text{ m}
$$

The distance of the rebound in the horizontal plane that contains the point of collision:

$$
d=\frac{v^{2} \sin 2 \alpha}{g}=2 s \sin 60^{\circ}=18.879 \text{ m}
$$

(Thiringer Aurél, Sopron.)

The problem was also solved by: Bálint B., Bauss O., Dénes A., Eislitzer Gy., Fekete J., Freund A., Goldstein Zs., Grünhut B., Hofbauer E., Iványi B., Kántor N., Klein M., Kreizler Gy., Krupecz V., Landler D., Mihálkovics E., Monoki Gy., Nagy O., Orlowszky F., Porde Gy., Riesz F., Schiffer H., Schólcz K., Szabó I., Szabó K., Szilágyi Z.