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anonymous
 3 years ago
If a stone is thrown down at 100 ft/s from a height of 1,250 feet, its height after t seconds is given by s = 1,250 − 100t − 16t^2
Estimate its instantaneous velocity at time t = 2
anonymous
 3 years ago
If a stone is thrown down at 100 ft/s from a height of 1,250 feet, its height after t seconds is given by s = 1,250 − 100t − 16t^2 Estimate its instantaneous velocity at time t = 2

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0We know that the equation for instantaneous velocity is \( f'(x)=\large \frac{f(x+h)f(x)}{(x+h)x}\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Are you familiar with this equation?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so \(f(t)=1250100t16t^2\) \(f(t+h)=1250100(t+h)16(t+h)^2\) so \(f'(x)= \large \frac{(1250100(t+h)16(t+h)^2)(1250100t16t^2)}{(x+h)x}\) \(f'(x)=\large \frac{1250100t100h16t^232th16h^21250+100t+16t^2}{h}\) \( f'(x)=\large \frac{100h32th16h^2}{h}\) \(f'(x)= \large \frac{h(10032t16h)}{h}\) \(f'(x)=(10032t16h)\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Ok Are you familiar with limits? Like what does f'(t) equal as h approaches 0?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Did ya follow so far?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Ok and keep in mind by accident I used X's in stead of T's so just ignore that

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1373424544924:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ok so the difference btwn x and x+h is just h

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Basically we have 2 points; x and x+h and we want them to beee sooooo close together So we want h to be realllllly small So we want h to be like nearly 0 Like the number right next to 0 So there is this method called limits and we limit the equation meaning we want to see what the equation will equal as h APPROACHES 0 \(\large f'(t)_{\lim h \to 0} 10032t16h\) Now there is only one term that has h in it which is 16h Now as h approaches 0 then 16h approaches 0 since 16*.00000000001=.00000000016 So its basically 0 so we consider it as if it is 0 and just trash that whole term \(\large f'(t)_{\lim h \to 0} 10032t16h=10032t\) Now we need to find the Instantaneous velocity when t=2 So we plug into our equation t=2 \(f'(2)=10032(2)=164

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So at t=2 the stone is travelling 164 ft/s downwards

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I hope you followed :)
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