To find the time of flight, determine the time the projectile takes to reach maximum height. The time of flight is just double the maximum-height time.

Start with the equation:

v_y = v_oy + a_y t

At maximum height, v_y = 0.

The time to reach maximum height is

t1/2

=

- voy ay

Time of flight is

t

=

2t1/2

=

-2voy ay

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

Time of flight is

t

=

2 vo sin(θ) g

where g = 9.8 m/s²

The time of flight is also determined solely by the initial velocity in the y direction and the acceleration due to gravity.

Three balls are launched straight up in the air. The ratio of their initial speeds is 1:2:3, in the order red:green:blue. What is the ratio of their times of flight, in the same order?

1. 9:4:1 (1/113) (1%)
2. 3:2:1 (19/113) (17%)
3. 1:2:3 (76/113) (67%)
4. 1:4:9 (17/113) (15%)
5. It depends on the ratio of their masses (0/113) (0%)