A projectile is thrown upward so that its distance above the ground after t seconds is h = -16t^2 + 672t. After how many seconds does it reach its maximum height?

Question

anonymous · Answer

Is it 42?

ddcamp · Answer

In quadratic functions (ax²+bx+c), the vertex (max or min, depending on the function) is at:
$$x=\frac{ -b }{ 2a }$$

ddcamp · Answer

The other way to solve it would be to find the time it takes to hit the ground again (h=0) and divide by 2.

anonymous · Answer

So it would be 21 if you did it the first way.

anonymous · Answer

Do you mean to set it equal to zero in the second one?

ddcamp · Answer

Yeah, set it equal ot 0

anonymous · Answer

If you did that, wouldn't you divide by 16, not 2?

ddcamp · Answer

No. Find t when h is 0. That will be the time when the projectile hits the ground again. At half that time is the maximum.

anonymous · Answer

So, is it 42, or 21?

ddcamp · Answer

42 would be when the ball hits the ground again, 21 would be when it's at its maximum.

anonymous · Answer

That's what I tought. Awesome. Thank you! God bless you. C: