Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

MarcLeclair

  • 2 years ago

A street light is mounted at the top of a 15 foot-tall pole. A man 6 ft tall walks away from the pole with the speed of 5 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?

  • This Question is Closed
  1. EulerGroupie
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'll say that x is the distance from the pole and s is the distance from the man to the tip of his shadow. The actual location of the shadow with respect to the pole would be x+s. The speed of the man would be dx/dt=5. |dw:1353905474708:dw| Using similar triangles...\[\frac{15}{x+s}=\frac{6}{s}\]\[15s=6(x+s)\]\[15s=6x+6s\]\[9s=6x\]\[s=\frac{6}{9}x=\frac{2}{3}x\]Differentiate with respect to time in order to find the rate of change of the shadow relative to the man.\[\frac{ds}{dt}=\frac{2}{3} \frac{dx}{dt}\]\[\frac{ds}{dt}=\frac{2}{3}(5)=\frac{10}{3}ft/s\]Now you could just add the rate of the man to the rate of the shadow... 10/3 +5=25/3 ft/s or you can use a little more calculus. From above, the location of the shadow is x+s. So after looking at the similar triangles, but keeping x and s together gives:\[x+s=\frac{15}{6}s=\frac{5}{2}s\] Taking the derivative here would give:\[\frac{d(x+s)}{dt}=\frac{5}{2} \frac{ds}{dt}\]Using our rate of change of the shadow from above (ds/dt=10/3):\[\frac{ds(x+s)}{dt}=\frac{5}{2} \frac{10}{3}=\frac{25}{3} ft/s\]Just like before.

  2. EulerGroupie
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    In that last line of equations... ignore the first s in ds(x+s). It was really meant to to be the derivative of x+s together with respect to time.

  3. MarcLeclair
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks :)_

  4. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.