Question
3) Amy hit a softball into the air at a speed of 39 ft/s. The height of the ball after t seconds is given by the function h(t) = -16t2 + 39t + 2
When does the softball reach its maximum height? (round to the nearest hundredth)
When does the softball reach its maximum height? (round to the nearest hundredth)
Answers
GPT 3.5
To find the maximum height of the softball, we need to determine the vertex of the parabolic function h(t) = -16t^2 + 39t + 2.
The formula for the x-coordinate of the vertex of a parabola in the form ax^2 + bx + c is given by x = -b/2a. In this case, a = -16 and b = 39.
So, x = -39 / (2*(-16)) = 39 / 32 ≈ 1.22
Now, we substitute this value back into the function h(t) to find the maximum height:
h(1.22) = -16(1.22)^2 + 39(1.22) + 2 ≈ 24.99
Therefore, the maximum height of the softball is approximately 24.99 feet, which occurs at t = 1.22 seconds.
The formula for the x-coordinate of the vertex of a parabola in the form ax^2 + bx + c is given by x = -b/2a. In this case, a = -16 and b = 39.
So, x = -39 / (2*(-16)) = 39 / 32 ≈ 1.22
Now, we substitute this value back into the function h(t) to find the maximum height:
h(1.22) = -16(1.22)^2 + 39(1.22) + 2 ≈ 24.99
Therefore, the maximum height of the softball is approximately 24.99 feet, which occurs at t = 1.22 seconds.