If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed and his hang time?
To determine Michael Jordan's takeoff speed and hang time, we'll need to make a few calculations.
First, let's start by finding the takeoff speed.
Takeoff speed is the initial velocity with which Michael Jordan leaves the ground. We can use the equation:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s at the peak of the jump)
u = initial velocity (takeoff speed)
a = acceleration due to gravity (-9.8 m/s^2)
s = displacement (vertical leap of 1.29 m)
Rearranging the equation to solve for u, we have:
u = √(v^2 - 2as)
Since v = 0 m/s, the equation simplifies to:
u = √(0^2 - 2(-9.8)(1.29))
Calculating this, we find:
u ≈ √(0 - 2(-9.8)(1.29)) ≈ √(25.284) ≈ 5.03 m/s
Therefore, Michael Jordan's takeoff speed is approximately 5.03 m/s.
Now, let's find the hang time, which is the amount of time Michael Jordan spends in the air.
Hang time can be calculated using the equation:
t = (v - u) / a
where:
t = time in seconds
v = final velocity (0 m/s at the peak of the jump)
u = initial velocity (takeoff speed)
a = acceleration due to gravity (-9.8 m/s^2)
Since we already know u and v, we can substitute them into the equation:
t = (0 - 5.03) / (-9.8)
Calculating this, we get:
t ≈ (-5.03) / (-9.8) ≈ 0.513 seconds
Therefore, Michael Jordan's hang time is approximately 0.513 seconds.
To calculate Michael Jordan's takeoff speed, you can use the following formula:
v = √(2 * g * h)
Where:
v represents the takeoff speed,
g represents the acceleration due to gravity (approximately 9.8 m/s²),
h represents the vertical leap (1.29 m).
Using these values:
v = √(2 * 9.8 * 1.29)
v ≈ 5.02 m/s
Therefore, Michael Jordan's takeoff speed is approximately 5.02 m/s.
To find the hang time, you can use the following formula:
t = (2 * v) / g
Where:
t represents the hang time,
g represents the acceleration due to gravity (approximately 9.8 m/s²),
v represents the takeoff speed (5.02 m/s).
Using these values:
t = (2 * 5.02) / 9.8
t ≈ 1.02 seconds
Therefore, Michael Jordan's hang time is approximately 1.02 seconds.