# The ball was thrown vertically upward at a speed V0. When it reached its highest point, another ball

**The ball was thrown vertically upward at a speed V0. When it reached its highest point, another ball was thrown also vertically upward, with the same initial speed. at what height they will collide.**

The kinetic energy of the ball at its highest point is converted into potential energy:

M V0 ^ 2/2 = M g H,

where M is the mass of the ball; V0 – initial speed; g is the acceleration of gravity; H is the maximum lifting height.

H = V0 ^ 2 / (2 g).

Equations of motion of balls from the moment of throwing the second ball:

the first: h = V0 t – gt ^ 2/2;

the second: h = H – gt ^ 2/2.

Equating h, we get:

V0 t = H; → t = Н / V0 = V0 / (2 g).

This means that the balls will collide at a height:

h = H −g t ^ 2/2 = V0 ^ 2 / (2 g) – V0 ^ 2 / (8 g) = 3V0 ^ 2 / (8 g).