Question

The trajectory of a golf ball hit from a tee on the ground at an angle of 40 degrees with an initial

speed of 50 meters per second can be modeled by the parabola f(x) = 0.84x - 0.0033x2, where the
x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance
the golf ball travels before hitting the ground.
PLEASE HELP ME IM USING ALL MY
POINTS

Answer 1

• 53.45 m
• 254.55 m

Explanation:

Given function:

• f(x) = 0.84x - 0.0033x²

Rewrite in the standard form:

• f(x) = - 0.0033x² + 0.84x

The maximum height is the vertex with x- coordinate -b/2a, which is:

• x = -0.84/2(-0.0033) ≈ 127.27

The highest point is:

• f(127.27) = -0.0033(127.27)² + 0.84(127.27) ≈ 53.45 m

The horizontal distance the golf ball travels before hitting the ground:

• f(x) = 0
• - 0.0033x² + 0.84x = 0
• 33x² - 8400x = 0
• x(33x - 8400) = 0
• x = 0- initial point
• 33x = 8400 ⇒ x = 8400/33 ≈ 254.55 m