Using a fireworks analogy, we launch a body upward with an initial velocity of $c=90 \mathrm{msec}^{-1}$; after $t=5$ seconds, we hear its explosion. At what height did it explode, if the speed of sound is $a=340 \mathrm{msec}^{-1}$? (Neglect air resistance.)
If a body explodes $x \mathrm{mp}$ later, then the distance covered by the body is:

$$
s=c x-\frac{1}{2} g x^{2}=(t-x) a
$$

from which

$$
x=\frac{1}{g}\left(a+c \pm \sqrt{(a+c)^{2}-2 a g t}\right)
$$

the root can only take a negative value, otherwise $x>t$, which is impossible. Thus,

$$
x=4.15 \mathrm{sec}
$$

and

$$
s=(t-x) a=289 \mathrm{~m}
$$

(Czank Károly, Déva.)

The problem was also solved by: Bayer B., Baumann J., Demeter J., Faith F., Filkorn J., Freudenberg K., Hein I., Holzmann M., Kerekes T., Krausz B, Krisztián Gy., Kürth A., Lukhaub Gy., Lupsa Gy., Perl Gy., Póka Gy., Sasvári G., Sasvári J., Scharff J., Singer A., Wohlstein S.