Question

A projectile is shot vertically from the ground level. It’s height h, in feet, after t seconds is given by h = 88t - 16t ^2. How long will it take the projectile to hit the ground ?

Answer 1

5.5 seconds.

Explanation:

The given function is

`h = 88t - 16t ^2`

where, h is height (in feet) of projectile after t seconds.

We need to find the time taken by projectile to hit the ground.

At ground level, the height of projectile is 0.

Substitute h=0 in the given function to find the time at which it hit the ground.

`0=88t - 16t ^2`

`0=8t(11 - 2t)`

Using zero product property we get

`8t=0\Rightarrow t=0`

`11-2t=0\Rightarrow t=(11)/(2)=5.5`

It mean projectile hits the ground at x=0 and x=5.5 seconds. We know that x=0 is the initial stage.

Therefore, so time taken by projectile to hit the ground is 5.5 seconds.

Answer 2

it will take 5.5 seconds to hit the ground

Explanation:

A projectile is shot vertically from the ground level. It’s height h, in feet, after t seconds is given by
`h = 88t - 16t ^2`

When the projectile hits the ground then the height becomes 0

`h = 88t - 16t ^2`

`0 = 88t - 16t ^2`

GCF is -8t

`0 = 8t(11 - 2t)`

now set each factor =0 and solve for t

`8t=0, t=0`

`11-2t=0, t=(11)/(2)`

So it will take 5.5 seconds to hit the ground