Question

A projectile is thrown upward so that its distance above the ground after t seconds is h = -16t2 + 672t. After how many seconds does it reach its maximum height?

Answer 1

calculus method or algebra method?

Answer 2

calculus

Answer 3

take the derivative, set the derivative = 0, then see what t is.

Answer 4

when the first derivative =0, a point is a local maximum or local minimum.

Answer 5

what is a derivative?

Answer 6

im in pre calc i have not gotten to that yet

Answer 7

oh, then you want the algebra method

Answer 8

yea i guess. sorry :/

Answer 9

find the points where x=0. since it is symmetric, the point exactly between the two zeroes will be the maximum

Answer 10

it's fine

Answer 11

so plug in points?

Answer 12

factor it

Answer 13

-16t(t+42)

Answer 14

so if you set that equal to zero,
0=-16t(t-42) you can see that either 16t or (t-42) has to equal 0 for the function to equal zero. (btw, you missed a sign change)

Answer 15

ok and now you solve for zero?

Answer 16

you know 16t = 0 or (t-42) = 0, solve for t in both cases. exactly between them will be the time where you have your maximum height

Answer 17

so it would be 21 because its in the middle of 0 and 42?

Answer 18

yep

Answer 19

thank you soo much!