Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

lexusbreon

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

  • 9 months ago
  • 9 months ago

  • This Question is Closed
  1. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    We know that the equation for instantaneous velocity is \( f'(x)=\large \frac{f(x+h)-f(x)}{(x+h)-x}\)

    • 9 months ago
  2. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    Are you familiar with this equation?

    • 9 months ago
  3. lexusbreon
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

    • 9 months ago
  4. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    so \(f(t)=1250-100t-16t^2\) \(f(t+h)=1250-100(t+h)-16(t+h)^2\) so \(f'(x)= \large \frac{(1250-100(t+h)-16(t+h)^2)-(1250-100t-16t^2)}{(x+h)-x}\) \(f'(x)=\large \frac{1250-100t-100h-16t^2-32th-16h^2-1250+100t+16t^2}{h}\) \( f'(x)=\large \frac{-100h-32th-16h^2}{h}\) \(f'(x)= \large \frac{h(-100-32t-16h)}{h}\) \(f'(x)=(-100-32t-16h)\)

    • 9 months ago
  5. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok Are you familiar with limits? Like what does f'(t) equal as h approaches 0?

    • 9 months ago
  6. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    Did ya follow so far?

    • 9 months ago
  7. lexusbreon
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes I follow so far

    • 9 months ago
  8. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok and keep in mind by accident I used X's in stead of T's so just ignore that

    • 9 months ago
  9. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1373424544924:dw|

    • 9 months ago
  10. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    ok so the difference btwn x and x+h is just h

    • 9 months ago
  11. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    Basically 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 \(\large f'(t)_{\lim h \to 0} -100-32t-16h\) 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 \(\large f'(t)_{\lim h \to 0} -100-32t-16h=-100-32t\) Now we need to find the Instantaneous velocity when t=2 So we plug into our equation t=2 \(f'(2)=-100-32(2)=-164

    • 9 months ago
  12. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    So at t=2 the stone is travelling -164 ft/s downwards

    • 9 months ago
  13. swissgirl
    Best Response
    You've already chosen the best response.
    Medals 1

    I hope you followed :)

    • 9 months ago
  14. lexusbreon
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank You so much!!

    • 9 months ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.