Respuesta :
Answer:
The option C) 15 s is correct
Therefore the maximum height it reaches in 15 seconds.
Step-by-step explanation:
Given equation is [tex]h =-13t^2 + 390t[/tex]
Given that a projectile is thrown upward so that its distance above the ground after t seconds is [tex]h =-13t^2 + 390t[/tex]
To find how many seconds does it reach its maximum height:
"The standard form of a parabola's equation is expressed as :
[tex]y=ax^2+bx+c[/tex].
If [tex]a>0[/tex], then the parabola opens upwards;
if [tex]a<0[/tex] the parabola opens downwards."
The maximum height is the vertex of the parabola [tex]h =-13t^2 + 390t[/tex] which is [tex]\frac{-b}{2a}[/tex].
Comparing the given equation with the standard form of parabola we get
the values of a=-13 , b=390 and c=0
The maximum height in [tex]t=\frac{-b}{2a}[/tex].
Substitute the values we get
[tex]t=-\frac{390}{2(-13)}[/tex]
[tex]=\frac{390}{26}[/tex]
[tex]=15[/tex]
