Since we have the formula for height, all we need to do is solve for t when the height of the ball is 0, meaning it is on the ground.
The equation is H = -16t^2 + 128t + 4
Substituting H for 0, we get: 0 = -16t^2 + 128t + 4
Now the problem becomes a simple quadratic equation that we can solve using the quadratic formula.
The quadratic formula for at^2 + bt + c = 0 is:
t = [-b +/- sqrt(b^2 - 4ac)] / 2a
Plugging in a, b, and c, we get
t = [-128 +/- sqrt(128^2 - 4*-16*4)] / -32
Solving for t, we get t = 8.03, -0.03. Since the time must be positive, the answer is 8.0. The ball is in the air for 8.0 seconds
