Answer: the ball's height is 14 feet when t = 2.5 seconds.
Step-by-step explanation: The height of the ball can be modeled by the following equation:
h = -16t^2 + 27t + 4
where:
h is the height of the ball
t is the time in seconds
-16 is the acceleration due to gravity
27 is the initial upward velocity
4 is the initial height
We want to find all values of t for which h = 14. This is equivalent to solving the following quadratic equation:
-16t^2 + 27t + 4 = 14
We can rewrite this equation as follows:
-16t^2 + 27t - 10 = 0
We can factor this equation as follows:
(-2t + 5)(8t - 2) = 0
Therefore, the solutions to the equation are t = 2.5 and t = 0.25.
However, we need to make sure that both of these solutions are physically valid. In other words, we need to make sure that the ball is actually in the air at both of these times.
We can see that the ball is in the air at t = 2.5 because the height of the ball is 14 feet at this time. However, we can see that the ball is not in the air at t = 0.25 because the height of the ball is negative at this time.
Therefore, the only valid solution to the equation is t = 2.5.
In conclusion, the ball's height is 14 feet when t = 2.5 seconds.