Question

A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 9 m/s. The height of the jumper can be modeled by (h(x) = -0.051x² + 0.364x), where (h) is the jumper's height in meters and (x) is the horizontal distance from the point of launch.

(a)At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places.

Answer 1

The maximum height of the long jumper occurs at approximately 3.57 meters from the point of launch, calculated using the vertex formula of a quadratic function.

Step-by-step explanation:

To find the horizontal distance from the point of launch at which the maximum height occurs for a long jumper modeled by the equation h(x) = -0.051x² + 0.364x, we need to determine the vertex of the parabola represented by this quadratic function. The x-coordinate of the vertex can be found using the formula -b/(2a), where a is the coefficient of the x² term and b is the coefficient of the x term. In this case, a = -0.051 and b = 0.364.

Plugging these values into the formula, we get:

x = -0.364 / (2 * -0.051) = -0.364 / -0.102 = 3.56863, which rounds to 3.57 meters.

Therefore, the maximum height occurs at a horizontal distance of approximately 3.57 meters from the point of launch.