Question

Derek threw a baseball across the field. The path of the ball can be represented by the equation h =-16t ² +75t+5, where t represents the number of seconds the ball was in the air, and h, represents the height of the ball in feet. the baseball was 2 feet above ground after how many seconds?

F 4.5 seconds
G 4.75 seconds
H 4.73 seconds
J 4.8 seconds

Answer 1

In order to solve this problem, we plug in 2 for h and then solve for t.


`2=-16 t^(2) +75t+5`

Next, we subtract 2 from both sides.


`-16 t^(2) +75t+3=0`

Now, we apply the quadratic formula.


`t= \frac{-75+- \sqrt{ 75^(2)-4*-16*3 } }{2*-16} = (-75+- √(5625+192) )/(-32) = (-75+- √(5817) )/(-32) = (-75+-76.27)/(-32)`

Now, we see what T is if we add 76.27 and if we subtract 76.27. First, let's try adding it.


`t= (-75+76.27)/(-32) = (1.27)/(-32) =-0.04`

Obviously, the ball was not in the air for a negative amount of side. Let's try subtracting 76.27.


`t= (-75-76.27)/(-32) = (-151.27)/(-32)=4.73`

Aha! We have found our answer. The ball was in the air for 4.73 seconds, so H is the correct answer.