Surprisingly, very few athletes can jump more than 2.0 ft (0.62 m) straight up. Use d = 1/2 gt2 and solve for the time one spends moving upward in a 2.0 foot vertical jump. Then double it for the "hang-time" -- the time one's feet are off the ground.
0.62 m = (1/2)gt^2
t = 0.336s
hang time = 2t = 0.71 s
Blake Griffin of the LA Clippers can do a lot better than that.
To solve for the time spent moving upward in a 2.0 foot vertical jump using the equation d = 1/2 gt^2, we can rearrange the equation as follows:
d = 1/2 gt^2
2.0 ft = 1/2 g(t)^2
where:
d = vertical distance (2.0 ft)
g = acceleration due to gravity (9.8 m/s^2 or 32.2 ft/s^2)
t = time spent moving upward
Let's solve for t:
2.0 ft = 1/2 * 32.2 ft/s^2 * (t)^2
4.0 ft = 16.1 ft/s^2 * (t)^2
Divide both sides by 16.1 ft/s^2:
(t)^2 = 4.0 ft / 16.1 ft/s^2
(t)^2 = 0.248447 ft/s^2
Take the square root of both sides to solve for t:
t = √(0.248447 ft/s^2)
t ≈ 0.4984 s
Now, to double the time spent moving upward for the "hang-time":
Hang-time = 2 * t
Hang-time ≈ 2 * 0.4984 s
Hang-time ≈ 0.9968 s
Therefore, the time one spends moving upward in a 2.0-foot vertical jump is approximately 0.4984 seconds, and the hang-time (time one's feet are off the ground) is approximately 0.9968 seconds.
To find the time one spends moving upward in a 2.0 ft vertical jump, we can use the formula:
d = (1/2) * g * t^2
Where:
d = distance (2.0 ft)
g = acceleration due to gravity (approximately 32.2 ft/s^2)
t = time
Rearranging the formula to solve for time (t), we have:
t^2 = (2 * d) / g
Substituting the given values, we have:
t^2 = (2 * 2.0 ft) / 32.2 ft/s^2
t^2 = 0.123 ft/s^2
Taking the square root of both sides to find t:
t ≈ √0.123 ≈ 0.351 seconds
This represents the time one spends moving upward in a 2.0 ft vertical jump.
To find the hang-time (the time one's feet are off the ground), we need to double the time:
Hang-time = 2 * t ≈ 2 * 0.351 ≈ 0.702 seconds.
Therefore, one spends approximately 0.351 seconds moving upward and has a hang-time of about 0.702 seconds during a 2.0 ft vertical jump.