Question

A bullet is fired straight up from a BB gun with initial velocity 1120 ft./s at an initial height of 8 feet. Use the formula h=-16t^2 +v0 t+8 to determine how many seconds it will take for the bullet to hit the ground. That is, when will h=0 ? Round your answer to the nearest whole number

Answer 1

So, time is 70 seconds

Explanation:

we are given equation of height as

`h(t)=-16t^2+v_0t+8`

we are given

initial velocity 1120 ft./s

so, we have

`v_0=1120ft/s`

now, we can plug it

`h(t)=-16t^2+1120t+8`

We will set h=0

and then we can solve for t

`h(t)=-16t^2+1120t+8=0`

we can use quadratic formula

`t=(-b\pm √(b^2-4ac))/(2a)`

`t=(-1120\pm √(1120^2-4\left(-16\right)8))/(2\left(-16\right))`

`t=-(√(4902)-70)/(2),\:t=(70+√(4902))/(2)`

`t=-0.00174,t=70.007`

we know that

time can never be negative

so, we get

`t=70.007`

Answer 2

Bullet will hit the ground after 70 seconds.

Explanation:

A bullet is fired straight up from a BB gun with initial velocity 1120 ft/s at an initial height of 8 ft.

`\text{Formula or Model of height }h(t)=-16t^2+1120t+8`

We need to find time when bullet hit the ground.

As we know when bullet hit the ground height would be 0

So, we set h=0 and solve for t .

`0=-16t^2+1120t+8`

Using quadratic formula

`t=(-1120\pm √((1120)^2-4(-16)(8)))/(2(-16))`

`t=70\text{ seconds}`

Thus, Bullet will hit the ground after 70 seconds.