Question

A ball is thrown vertically upward from the top of a 200 foot tower, with an initial velocity of 5 ft/sec. Its position function is s(t) = –16t2 + 5t + 200. What is its velocity in ft/sec when t = 3 seconds?

Answer 1

Guys please Help me

Answer 2

@radar could you please help me?

Answer 3

@robtobey

Answer 4

take the derivative and plug in 3 for t

Answer 5

is that how you find the distance? @sourwing

Answer 6

no. velocity

Answer 7

WHT DO YOU MEAN BY DERIVATE?

Answer 8

@sourwing ?

Answer 9

Guys please help me

Answer 10

@chrisdbest

Answer 11

Answer to a similar question - http://www.algebralab.org/Word/Word.aspx?file=Algebra_MaxMinProjectiles.xml

Answer 12

they're similar but they talk about the maximums @Kash_TheSmartGuy

Answer 13

Oh ok.

Answer 14

do you know someone that could help me? @Kash_TheSmartGuy

Answer 15

Probably @jim_thompson5910 or @campbell_st

Answer 16

@jim_thompson5910 could you help me?

Answer 17

this is for calculus class right?

Answer 18

yes

Answer 19

have you learned about derivatives? or differentiation?

Answer 20

No I haven't, but my professor explained that it was related to the slope formula

Answer 21

that's the average velocity, but they want the instantaneous velocity here

Answer 22

it seems odd how he's asking about a topic you haven't learned about yet

Answer 23

Wait I checked my notes isn't f(x) lim x-->0 f(a-h)-f(a) / h

Answer 24

yes it is

Answer 25

that's the limit definition of the derivative

Answer 26

okay, but what could I first?

Answer 27

Do I plug the 3 in the A right

Answer 28

yes

Answer 29

what are f(3) and f(3+h) equal to

Answer 30

btw that should be f(a+h) and not f(a-h)

but I guess it doesn't matter if h goes to 0

Answer 31

F(3) gives me 71
and F(a+h) gives me h^2+6h+9

Answer 32

f(3) is correct but what you got for f(3+h) is not correct

Answer 33

isn't -144-96h-16h^2

Answer 34

f(t) = -16t^2+5t+200


f(3+h) = -16(3+h)^2+5(3+h)+200


f(3+h) = -16(9+6h + h^2)+5(3+h)+200


f(3+h) = -144-96h-16h^2+15+5h+200


f(3+h) = -16h^2-91h+71

Answer 35

Use

f(3) = 71
f(3+h) = -16h^2-91h+71

to find

\[\Large \frac{f(3+h)-f(3)}{h}\]

Answer 36

okay i see my mistake

-91

Answer 37

yep

\[\Large \frac{f(3+h)-f(3)}{h}=\frac{-16h^2-91h+71-71}{h}\]
\[\Large \frac{f(3+h)-f(3)}{h}=\frac{-16h^2-91h}{h}\]
\[\Large \frac{f(3+h)-f(3)}{h}=\frac{h(-16h-91)}{h}\]
\[\Large \frac{f(3+h)-f(3)}{h}=\frac{\cancel{h}(-16h-91)}{\cancel{h}}\]

Then plug in h = 0 to get -16h-91 to turn into -91

Answer 38

at that instant in time, the object is going -91 ft/sec (ie it's falling at 91 ft/sec)

Answer 39

okay, OMG thank you very muchI will write this down about the instantaneous velocity formula. I really appreciate all your help, god will pay you in a way that you will feel blessed. thank you, I had to submit this today at 12 and I am ready, thank you so much

Answer 40

you're welcome, I'm glad it helped out