Question

A golfer hits a golf ball.

Answer 1

Answer:

The golf ball was in the air for 4 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$.

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$, given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

In this question:

We have to find the amount of time it takes for the ball to hit the ground. We have that:

$d(t) = -2t^2 + 7t + 4$

Which is a quadratic equation with $a = -2, b = 7, c = 4$.

How long is the golf ball in the air?

We have to find t for which $d(t) = 0$

So

$-2t^2 + 7t + 4 = 0$

$\Delta = b^{2} - 4ac = (7)^2 - 4(-2)(4) = 81$

$t_{1} = \frac{-7 + \sqrt{81}}{2*(-2)} = -0.5$

$t_{2} = \frac{-7 - \sqrt{81}}{2*(-2)} = 4$

Time is a positive measure, so t = 4.

The golf ball was in the air for 4 seconds.