Question

A projectile is thrown upward so that it's distance above the ground after t seconds is h=-16t^2 +672t. After how many seconds does it reach its maximum height?

Answer 1

It will reach its maximum height at the vertex of the parabola. Which is always:

(-b/(2a), (4ac-b^2)/(4a))

So the time when this occurs is the x coordinate, or t in this case.

-b/(2a), and b=672 and a=-16 so

t=-672/-32

t=21 seconds

Answer 2

Answer: 21 seconds

Explanation:

We know that a parabola with equation
`y=ax^2+bx+c` attains its maximum height at :-

`x=(-b)/(2a)`

The given function:
`h=-16t^2 +672t`

It will attain its maximum height at :

`t=(-672)/(2(-16))=21`

Hence , after 21 seconds the projectile will reach its maximum height .