## anonymous one year ago A ball is thrown vertically upward from the top of a 100-foot tower, with an initial velocity of 20 ft/sec. Its position function is s(t) = –16t2 + 20t + 100. What is its velocity in ft/sec when t = 1 second? –12 –44 100 –32

1. anonymous

C. 100

2. anonymous

how did you get that?

3. anonymous

If i plug t=1 into the equation I get 104, which isn't an answer

4. anonymous

@zzr0ck3r

5. anonymous

@carlyleukhardt

6. anonymous

huh?

7. anonymous

8. anonymous

It was wrong @carlyleukhardt

9. Photon336

@graze65 you need to visualize this first with a figure

10. Photon336

|dw:1443474354027:dw|

11. Photon336

The height of our tower is 100 ft and the ball was thrown at an initial velocity of 20ft/second another thing to add that equation gives you the position not the velocity. 32.1 ft/second is the acceleration due to gravity and that's downward.

12. anonymous

so, what do I do next? Do I use the equation for anything? I know I can use the final velocity= initial + (acceleration x speed)

13. Photon336

I came up with two possible solutions I'll show you both of them hopefully this will give us the answer

14. Photon336

This gives is the equation for the position with respect to time. but we're asked for the velocity with respect to time. $s(t) = -16t ^{2} +20t + 100$ if we take the derivative, differentiate this position with respect to time we get velocity $\frac{ D(s) }{ dT } = -32t + 20$ we plug in one second Vf = we get -32(1) + 20 = -12 ft/second Second way. we use the formula $V_{o} + at = V_{f}$ we convert 9.8 meters/second squared to feet per second squared and get 32.1 ft/second squared for the acceleration. the acceleration is pointing down. 20ft/second - 32.1ft/second squared (1second) = -12 ft/second squared = vf the negative means the velocity is going down so our ball/object is going downwards.

15. Photon336

you notice something though, when i took the derivative i got the same kinematic formula.

16. anonymous

OHHHHHH I get it now

17. anonymous

thank you so much! gonna medal and fan you

18. Photon336

no problem :) @graze65 have you taken calculus I? this is why derivatives come in handy.

19. anonymous

I'm in calculus now :) this was a calc problem.

20. Photon336

$\frac{ dS }{ dT } = \frac{ \Delta position }{ \Delta time } = velocity$