anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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carlyleukhardt
  • carlyleukhardt
C. 100
anonymous
  • anonymous
how did you get that?
anonymous
  • anonymous
If i plug t=1 into the equation I get 104, which isn't an answer

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More answers

anonymous
  • anonymous
@zzr0ck3r
anonymous
  • anonymous
@carlyleukhardt
carlyleukhardt
  • carlyleukhardt
huh?
anonymous
  • anonymous
how did you get that answer? can you please explain?
anonymous
  • anonymous
It was wrong @carlyleukhardt
Photon336
  • Photon336
@graze65 you need to visualize this first with a figure
Photon336
  • Photon336
|dw:1443474354027:dw|
Photon336
  • 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.
anonymous
  • 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)
Photon336
  • Photon336
I came up with two possible solutions I'll show you both of them hopefully this will give us the answer
Photon336
  • 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.
Photon336
  • Photon336
you notice something though, when i took the derivative i got the same kinematic formula.
anonymous
  • anonymous
OHHHHHH I get it now
anonymous
  • anonymous
thank you so much! gonna medal and fan you
Photon336
  • Photon336
no problem :) @graze65 have you taken calculus I? this is why derivatives come in handy.
anonymous
  • anonymous
I'm in calculus now :) this was a calc problem.
Photon336
  • Photon336
\[\frac{ dS }{ dT } = \frac{ \Delta position }{ \Delta time } = velocity\]

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