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 Use the quadratic formula.

Answer 1

We want to find the time when the height, 𝑦, is zero, since this would indicate that the golf ball has landed on the ground.

Setting 𝑦 equal to zero in the given equation, we get:

0 = −5𝑥2 + 20𝑥 + 0.05

Now we can use the quadratic formula:

𝑥 = (−𝑏 ± √(𝑏^2 − 4𝑎𝑐))/2𝑎

Where 𝑎 = −5, 𝑏 = 20, and 𝑐 = 0.05.

Plugging in these values, we get:

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

Simplifying:

𝑥 = (−20 ± √(400.25))/−10

𝑥 ≈ 0.005 seconds or 𝑥 ≈ 3.995 seconds

The negative value doesn't make sense in this context, so we can discard it. Therefore, the golf ball is in the air for approximately 3.995 seconds.