Question

if a ball is thrown vertically upward with a velocity of 80ft/s, then its height after t seconds is s=80t-26t^2.
how do i find the maximum height reached by the ball?

Answer 1

For some reason I was thinking s was velocity. :-/

Answer 2

OOps, wrong!
x = 80/ 52 = 1.5 ft

Answer 3

@Chlorophyll what's your method?

Answer 4

And what does s represent? Distance?

Answer 5

maximum of parabola has vertex ( x = -b/2a, y = f ( -b/2a ) )

Answer 6

oh okay... for some reason I was thinking about kinematics equations.

Answer 7

Yes, "its heigt = s..."

Answer 8

take the first derivative of s (80-52t) find the zero (1.5384615) that is the time at which te height is reaced then plug that into the original equation its 61.53 ft

Answer 9

Derivative's used for calculus level, while vertex applies for algebra level!

Answer 10

It's so tempting to use calc for these problems

Answer 11

it gives the same answer im just usingthe esiest way for me to do you could always jsut graph the quadratic and find the maximum either way is the same

Answer 12

kinematics

Answer 13

But then I remember all those kinematics equations from physics and keep thinking I need to use those (banging head on desk right now).

Answer 14

Yep, but I'm unsure if the asker at that level .

Answer 15

It's gotta be algebra level. I remembered having to do probs like these 6 yrs ago when I took it.

Answer 16

I'm horrible at Physics, teach me some day, will you, people !

Answer 17

no matter how you do it its 61.53846 to 7 sig figs lol

Answer 18

Why don't we just find the vertex of the parabola.

\[{\rm \max~height} = {-b \over 2a}\]

Answer 19

80/52

Answer 20

that solves for x and the question wants y so you still have to plug that into the original equation to find theheight not the time that that height occurs

Answer 21

Then plug it back in and solve for s.

Answer 22

it's calculus and i noticed i wrote the equation wrong its s=80t-16t^2 and i think i figured it out, i first took the derivative of it which was v(t)= 80-32t then solved for 0 because the velocity at max is zero then i plugged what i found for t into the original equation which was 2.5 so it was 80(2.5)-16(2.5)^2 and it ends up to be 100ft

Answer 23

that sthe correctway to do the problem, and yes changing 26 to 16 will change the answer LOL

Answer 24

for this same equation, i need to find the velocity of the ball when its at 96 ft above the ground on its way up and its way down?

Answer 25

differentiate the equation again to find the acceleration, then use v=u+at