Final answer:
By setting the height equation h(t) = -16t² + 60t + 2 equal to 64 and rearranging to form a quadratic equation, we can determine if the ball reaches 64 feet. The discriminant of the resulting quadratic equation is negative, indicating no real solutions and therefore the ball does not reach 64 feet in height.
Step-by-step explanation:
To determine if the ball reaches a height of 64 feet, we need to see if the equation h(t) = -16t² + 60t + 2 has a solution when h(t) = 64. We can find this out by setting the equation equal to 64 and solving for t:
64 = -16t² + 60t + 2
By rearranging the equation to set it to zero, we get:
-16t² + 60t + 2 - 64 = 0
-16t² + 60t - 62 = 0
Now, we use the quadratic formula, t = (-b ± √(b² - 4ac)) / (2a), where a = -16, b = 60, and c = -62. Calculating the discriminant (b² - 4ac) we find:
(60)^2 - 4(-16)(-62) = 3600 - 3968 = -368
A negative discriminant indicates that there are no real solutions to the equation, which means the ball does not reach a height of 64 feet. Hence, the ball will not reach the height of 64 feet since the quadratic equation does not have real solutions.