Question

a tee box is 128 feet above its fairway. When a golf ball is hit from the tee box with an initial vertical velocity of 32 ft/s, the quadratic equation 0=-16t^2+32t+128 gives the time in seconds when a golf ball is at height 0 fee on the fairway solve the quadratic equation by factoring to see how long the ball id in the air

Answer 1

Given:

A tee box is 128 feet above its fairway. When a golf ball is hit from the tee box with an initial vertical velocity of 32 ft/s, the quadratic equation
`0=-16t^2+32t+128` gives the time in seconds when a golf ball is at height 0 feet on the fairway.

We need to determine the time that ball is in the air.

Time taken:

The time can be determined by factoring the quadratic equation.

Thus, we have;

`-16t^2+32t+128=0`

Let us solve the equation using the quadratic formula,

`x=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}`

Substituting
`a=-16, b=32, c=128` in the above formula, we get;

`t=\frac{-32 \pm \sqrt{32^(2)-4(-16) 128}}{2(-16)}`

`t=(-32 \pm √(1024+8192))/(-32)`

`t=(-32 \pm √(9216))/(-32)`

`t=(-32 \pm 96)/(-32)`

Thus, the roots of the equation are

`t=(-32+96)/(-32)` and
`t=(-32-96)/(-32)`

`t=(64)/(-32)` and
`t=(-128)/(-32)`

`t=-2` and
`t=4`

Since, the value of t cannot be negative, thus, the value of t is
`t=4`

Hence, the ball is in the air for 4 seconds.