Question

A baseball is thrown up into the air. The ball's height in feet is modeled by the equation h(t) = -16t2 + 32t + 10. (h = height, t = time in seconds)
Find the maximum height of the ball.
a) 10 feet
b) 2.3 feet
c) 23 feet
d) 26 feet

Answer 1

Do you know how to take derivative?

Answer 2

differentiate
h' = -32t + 32 = 0
t = 1

plug 1 into your formula for h(t) and you have it

Answer 3

use formula when x=(-b/2a), y will have a max/min. in this quadratic equation, it has the max.
x=(-b/2a)=-32/(2*-16)=1
and then, substitude x=1 into the equation.
u can get max y=26

Answer 4

did u get it?

Answer 5

I know this is basically what Andrew said, but I am just trying to give an intuition on how it works. Since we know the ball will spend them amount of time going up as it does going down we know that the halfway point between the zeros of the function will be the maximum. So if we solve for the root and then add the roots together and divide by 2 we get the halfway point which is 1.
Roots --> ((1/4)(4-(26)^(1/2))+(1/4)(4+(26)^(1/2))) = 2 and 2/2 is 1.
H must reach a max at t=1 so plug this back into the formula like all the others said and you get your answer. Just a different way of thinking about problem.

Answer 6

the same amount of time**

Answer 7

@Andrewnj ya i get it thanks

Answer 8

@mathdood thanks a lot :)

Answer 9

26 feet.. any doubt
?

Answer 10

so u guys think the answer is 26 for sure ???? :)

Answer 11

do u understand?

Answer 12

not really :)

Answer 13

k.if t=1 then -16(1)^2 + 32(1) + 10=26
if t is equal to more then 1, there will be lesser amount then 26.
eg: -16(2)^2 + 32(2) + 10=10

eg: -16(3)^2 + 32(3) + 10=-38
so time should be less, bt time cant be a minus figure becouse of dat i took t=1.

did u get it?

Answer 14

It would be easiest if you understand differentiation. Do you? If not finding the midpoint of the roots is simpler but more tedious.

Answer 15

didnt get it..

Answer 16

suppose u hav y=x^n
then its differentiation dy/dx will be nx^(n-1)
differentiation of a number is zero.
and if u hav y=nx
its differentiation dy/dx will be n.
is t clear upto this?

Answer 17

@this r u there?

Answer 18

yes @ ajprincess

Answer 19

@ILM.Riyas finally i got it thanks a lot:D

Answer 20

thanks ya'all r the best :)

Answer 21

yw:)

Answer 22

@ this
always welcome