In order to solve this problem, we plug in 2 for h and then solve for t.
[tex]2=-16 t^{2} +75t+5[/tex]
Next, we subtract 2 from both sides.
[tex]-16 t^{2} +75t+3=0[/tex]
Now, we apply the quadratic formula.
[tex]t= \frac{-75+- \sqrt{ 75^{2}-4*-16*3 } }{2*-16} = \frac{-75+- \sqrt{5625+192} }{-32} = \frac{-75+- \sqrt{5817} }{-32} = \frac{-75+-76.27}{-32} [/tex]
Now, we see what T is if we add 76.27 and if we subtract 76.27. First, let's try adding it.
[tex]t= \frac{-75+76.27}{-32} = \frac{1.27}{-32} =-0.04[/tex]
Obviously, the ball was not in the air for a negative amount of side. Let's try subtracting 76.27.
[tex]t= \frac{-75-76.27}{-32} = \frac{-151.27}{-32}=4.73 [/tex]
Aha! We have found our answer. The ball was in the air for 4.73 seconds, so H is the correct answer.
