How to Find the Maximum Height Reached by a Diablo Thrown Vertically Upwards
What is the function representing the height reached by the diablo over time?
The height h reached by the diablo is expressed by the function h(t)=-t²+39.3t.
How can we determine the maximum height reached by the diablo?
What is the process to find the maximum height of the diablo?
Function and Maximum Height
The function representing the height reached by the diablo over time is h(t)=-t²+39.3t. To determine the maximum height reached by the diablo, we need to find the vertex of the parabolic function.
When a person throws a diablo vertically upwards with a certain speed, the height reached by the diablo is given by the function h(t)=-t²+39.3t. To find the maximum height reached by the diablo, we need to locate the vertex of the parabolic function.
The formula for the vertex of a parabola in the form y = ax^2 + bx + c is (-b/2a, c - b^2/4a). In this case, a = -1, b = 39.3, and c = 0. By substituting these values into the formula, we find that the time at which the diablo reaches its maximum height is tmax = -39.3/(2(-1)) = 19.65.
Subsequently, to determine the maximum height, we substitute the obtained time value back into the original equation: hmax = - (19.65)^2 + 39.3(19.65) ≈ 39.15 meters. Therefore, the maximum height reached by the diablo is approximately 39.15 meters.