Answer:
Bullet will hit the ground after 70 seconds.
Step-by-step explanation:
A bullet is fired straight up from a BB gun with initial velocity 1120 ft/s at an initial height of 8 ft.
[tex]\text{Formula or Model of height }h(t)=-16t^2+1120t+8[/tex]
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 .
[tex]0=-16t^2+1120t+8[/tex]
Using quadratic formula
[tex]t=\dfrac{-1120\pm \sqrt{(1120)^2-4(-16)(8)}}{2(-16)}[/tex]
[tex]t=70\text{ seconds}[/tex]
Thus, Bullet will hit the ground after 70 seconds.
Answer:
So, time is 70 seconds
Step-by-step explanation:
we are given equation of height as
[tex]h(t)=-16t^2+v_0t+8[/tex]
we are given
initial velocity 1120 ft./s
so, we have
[tex]v_0=1120ft/s[/tex]
now, we can plug it
[tex]h(t)=-16t^2+1120t+8[/tex]
We will set h=0
and then we can solve for t
[tex]h(t)=-16t^2+1120t+8=0[/tex]
we can use quadratic formula
[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]t=\frac{-1120\pm \sqrt{1120^2-4\left(-16\right)8}}{2\left(-16\right)}[/tex]
[tex]t=-\frac{\sqrt{4902}-70}{2},\:t=\frac{70+\sqrt{4902}}{2}[/tex]
[tex]t=-0.00174,t=70.007[/tex]
we know that
time can never be negative
so, we get
[tex]t=70.007[/tex]
