Answer:
7 seconds
Step-by-step explanation:
A firecracker shoots up from a hill 140 feet high with an initial speed of 100 feet per second. Using the formula H(t) = −16t^2 + vt + s
v is the initial speed and s is the initial height
Initial speed v= 100 and initial height = 140
So the equation becomes H(t) = −16t^2 + 100t + 140
When the firecracket hit the ground the height becomes 0
So we plug in H(t) for 0 and solve for t
[tex]0 = -16t^2 + 100t + 140[/tex]
Apply quadratic formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a= -16, b= 100, c= 140
[tex]t=\frac{-100+-\sqrt{100^2-4(-16)(140)}}{2(-16)}[/tex]
[tex]t=\frac{-100+-\sqrt{18960}}{-32}[/tex]
[tex]t=\frac{-100+-\4sqrt{1185}}{-32}[/tex]
[tex]t=\frac{25+-\sqrt{1185}}{8}[/tex]
t=-1.18 or t= 7.43
it take 7 seconds for the firecracker to hit the ground
