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.
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?
1 answer
3 answers