Question

A painter working at 100 feet from the ground drops his paint brush onto the street below. The function, s(t)=-16t^2+100, gives the height in feet of the paint brush as it falls to the ground. The velocity at time t=2 seconds is given by lim t->2 s(2)-s(t)/(2-t). Evaluate this limit to find the velocity of the paint brush at 2 seconds.

Answer 1

http://screensnapr.com/v/qU586F.png

Answer 2

Just to make clear what the equation is.

Answer 3

@satellite73

Answer 4

@amistre64 my hero?

Answer 5

@saifoo.khan @Hero anyone D:

Answer 6

dont we have to differentiate the distance equation to get the equation for velocity?

Answer 7

I feel like I just called up the justice league of the smartest people ever at math..

Answer 8

i think its asking for first principles

Answer 9

yes we could cheat and take the derivative and replace t by 2, but lukecrayons hasn't gotten there yet in calc, so we have to grind it out

Answer 10

Ah. okays..

Answer 11

What level of math is that? @Lukecrayonz

Answer 12

Precalculus, the final chapter, Introduction to calculus.

Answer 13

-64

Answer 14

We can do it the easier way if we are doing calc. ;)
But you aren't. :l

Answer 15

\[s(t)=-16t^2+100\]
\[s(2)=36\]
\[s(t)-s(2)=-16t^2+100-36=-16t^2+64\]
\[=-16(t^2-4)=-16(t+2)(t-2)\]

Answer 16

lol^

Answer 17

-64 ft/s

Answer 18

so
\[\frac{s(2)-s(t)}{2-t}=\frac{16(2-t)(2+t)}{2-t}\]\]
\[=16(2+t)\] take the limit as t goes to 2, get
\[16(2+2)=16\times 4=64\]

Answer 19

something like that
should be negative though, because it is falling

Answer 20

yes
it's negative

Answer 21

you forgot a sign -

Answer 22

Hey is latex working? D:

Answer 23

@saifoo.khan yes

Answer 24

never stopped for me
must be you!

Answer 25

Thank you all!

Answer 26

This is what i am getting from a long time.

Answer 27

I will try to reload.

Answer 28

Since you guys are here.. I have another question..

Answer 29

http://screensnapr.com/v/caYPLG.png

Answer 30

actually I'll repost.