The maximum height, y_max, can be found from the equation:

v_y ² = v_oy² + 2 a_y (y - y_o)

y_o = 0, and, when the projectile is at the maximum height, v_y = 0.

Solving the equation for y_max gives:

ymax

=

- voy2 2 ay

Plugging in v_oy = v_o sin(θ) and a_y = -g, gives:

ymax

=

vo2sin2(θ) 2 g

where g = 9.8 m/s²

The maximum height is determined solely by the initial velocity in the y direction and the acceleration due to gravity. It's not affected by what's happening in the x direction.

Two balls are launched straight up into the air. The green ball has an initial velocity twice as large as the red ball's initial velocity. Compare the maximum heights reached by the two balls (neglect air resistance).

1. The red ball goes 4 times higher
2. The red ball goes 2 times higher
3. The balls reach the same height
4. The green ball goes 2 times higher
5. The green ball goes 4 times higher
6. It depends on how their masses compare