A community for students.
Here's the question you clicked on:
 0 viewing
 one year 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
 one year 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

This Question is Closed

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1We know that the equation for instantaneous velocity is \( f'(x)=\large \frac{f(x+h)f(x)}{(x+h)x}\)

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1Are you familiar with this equation?

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1so \(f(t)=1250100t16t^2\) \(f(t+h)=1250100(t+h)16(t+h)^2\) so \(f'(x)= \large \frac{(1250100(t+h)16(t+h)^2)(1250100t16t^2)}{(x+h)x}\) \(f'(x)=\large \frac{1250100t100h16t^232th16h^21250+100t+16t^2}{h}\) \( f'(x)=\large \frac{100h32th16h^2}{h}\) \(f'(x)= \large \frac{h(10032t16h)}{h}\) \(f'(x)=(10032t16h)\)

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1Ok Are you familiar with limits? Like what does f'(t) equal as h approaches 0?

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1Did ya follow so far?

lexusbreon
 one year ago
Best ResponseYou've already chosen the best response.0Yes I follow so far

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1Ok and keep in mind by accident I used X's in stead of T's so just ignore that

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1dw:1373424544924:dw

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1ok so the difference btwn x and x+h is just h

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1Basically 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

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1So at t=2 the stone is travelling 164 ft/s downwards

swissgirl
 one year ago
Best ResponseYou've already chosen the best response.1I hope you followed :)

lexusbreon
 one year ago
Best ResponseYou've already chosen the best response.0Thank You so much!!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.