Question
This same rock is thrown and it follows the path modeled by the function: h(t) = −16t^2 + 50t + 20
(2 points) When does the rock reach it's maximum height? Response area
What is the maximum height it reaches?
(2 points) When does the rock reach it's maximum height? Response area
What is the maximum height it reaches?
Answers
GPT 3.5
The rock reaches its maximum height at the vertex of the parabolic function h(t) = -16t^2 + 50t + 20. To find the t-value at the vertex, we can use the formula t = -b / 2a, where a = -16 and b = 50 in this case.
t = -50 / (2*(-16))
t = -50 / (-32)
t = 1.5625
So, the rock reaches its maximum height at t = 1.5625 seconds.
To find the maximum height reached by the rock, we can substitute t = 1.5625 back into the function:
h(1.5625) = -16(1.5625)^2 + 50(1.5625) + 20
h(1.5625) = -16(2.4414) + 78.125 + 20
h(1.5625) = -39.0584 + 98.125 + 20
h(1.5625) = 79.0666
Therefore, the rock reaches a maximum height of approximately 79.07 feet.
t = -50 / (2*(-16))
t = -50 / (-32)
t = 1.5625
So, the rock reaches its maximum height at t = 1.5625 seconds.
To find the maximum height reached by the rock, we can substitute t = 1.5625 back into the function:
h(1.5625) = -16(1.5625)^2 + 50(1.5625) + 20
h(1.5625) = -16(2.4414) + 78.125 + 20
h(1.5625) = -39.0584 + 98.125 + 20
h(1.5625) = 79.0666
Therefore, the rock reaches a maximum height of approximately 79.07 feet.