Respuesta :
When the firecracker hits the ground, H(t) = 0.0 = -16t^2 + 90t + 160Using the quadratic formula,t = (-90 +- sqrt(90^2 - 4(-16)(160))) / 2(-16)t = -1.42 ort = 7.04
The negative time is extraneous. Therefore,t = 7.04 s.
The negative time is extraneous. Therefore,t = 7.04 s.
Answer : t = 7.044 sec
Explanation :
It is given that,
Velocity, [tex]v=90\ feet/sec[/tex]
distance, [tex]s=160\ m[/tex]
[tex]H(t)=-16\ t^2+ vt+ s[/tex]
When firecracker hits the ground hen H(t) = 0
So, [tex]-16 t^2+90\ t+160=0[/tex]
or
[tex]8 t^2-45\ t-80=0[/tex]
Solving this quadratic equation, we get
[tex]t=\dfrac{-(-45) \pm \sqrt{(-45)^2-4(8)(-80)} }{2(8)}[/tex]
[tex]t=\dfrac{45\ \pm\sqrt{4585} }{16}[/tex]
[tex]t=7.044\ sec[/tex]
Neglecting negative values as time can't be negative.
Firecracker will take 7.044 sec to hit the ground.
