Question

A golf ball is hit from the top of a tee. The quadratic equation
𝑦 = −5𝑥2 + 20𝑥 + 0.05 describes its height, 𝑦, in metres as time, 𝑥, in seconds
passes. Determine how long the ball is in the air t:
Use the quadratic formula.

Answer 1

To determine how long the ball is in the air, we need to find when its height (y) is equal to zero. This is because when the ball hits the ground, its height is zero.

So, we set the quadratic equation equal to zero:

-5x^2 + 20x + 0.05 = 0

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = -5, b = 20, and c = 0.05

x = (-20 ± √(20^2 - 4(-5)(0.05))) / 2(-5)

x = (-20 ± √(400 + 1))/(-10)

x = (-20 ± √401)/(-10)

x = (-20 + √401)/(-10) or x = (-20 - √401)/(-10)

x ≈ 0.1013 or x ≈ 3.8987

Since the ball cannot be in the air for a negative time, we discard the negative solution.

Therefore, the ball is in the air for approximately t = 0.1013 seconds.