DeSean throws a ball up with an initial vertical velocity of 30 feet per second from a platform that is at ground level. How long will the ball be in the air?
h=ho+vi*t-4.9t^2
h=ho=0
0=vi*t-4.9t^2= t(vi-4.9t)
t= 30/4.9 m/s
To determine how long the ball will be in the air, we can use the fact that the vertical displacement of the ball at the highest point of its trajectory will be zero. We can use the equation:
vf = vi + at
Where:
- vf is the final velocity (which will be zero when the ball is at its highest point)
- vi is the initial velocity (given as 30 feet per second)
- a is the acceleration due to gravity (which is approximately -32 feet per second squared)
- t is the time
Plugging in the given values into the equation:
0 = 30 + (-32)t
Simplifying the equation:
-32t = -30
Dividing both sides by -32:
t = -30 / -32
t ≈ 0.9375
Therefore, the ball will be in the air for approximately 0.9375 seconds.