Question

A long jumper leaves the ground at an angle above the horizontal, at a speed of 9m/s. The height of the jumper can be modeled by h(x) = -0.049x^2 + 0.366x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch. At what horizontal distance from the point of launch does the maximum height occur?

Answer 1

The maximum height of a long jumper's trajectory, described by a quadratic function, occurs at the vertex of the parabola, which is at about 3.73 meters from the point of launch.

Step-by-step explanation:

The maximum height of the jumper's arc, described by the function h(x) = -0.049x^2 + 0.366x, occurs at the vertex of the parabola. To find the horizontal distance at which the maximum height occurs, we use the formula for the x-coordinate of the vertex of a parabola, which is -b/(2a). Here, a is the coefficient of x^2, which is -0.049, and b is the coefficient of x, which is 0.366.

Plugging these values into the formula, we get:

x = -0.366 / (2 * -0.049) = -0.366 / -0.098 = 3.73469 meters

Therefore, the long jumper reaches the maximum height at a horizontal distance of approximately 3.73 meters from the point of launch.