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).
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