Final answer:
To find the maximum height of an object's parabolic trajectory, we calculate the vertex's x-coordinate using -b/(2a) from the given equation y=280x-16x², then substitute it back to find the y-coordinate, which is the maximum height, resulting in 233 meters.
Step-by-step explanation:
The student's question pertains to finding the maximum height of an object following a parabolic trajectory, described by the equation y = 280x - 16x². To determine the maximum height, we need to find the apex of the trajectory, which occurs when the vertical velocity component (Vy) is zero.
We can approach this problem by finding the vertex of the parabola in the equation provided, which represents the highest point.
To find the vertex, we use the formula for the vertex of a parabola given by y = ax² + bx + c, in which the x-coordinate of the vertex, which shows the time at which the maximum height is reached, is -b/(2a). In the given equation, a is -16 and b is 280, so the x-coordinate of the vertex is -280/(2 * -16). After finding the x-coordinate, we can substitute it back into the original equation to find the corresponding y-coordinate, which would be our maximum height.
Carrying out the calculation gives us the x-coordinate of the vertex as 8.75. We then evaluate the equation y = 280x - 16x² at x = 8.75 to obtain the maximum height which is y = 233 meters.