What is the speed of sprinter running away from lens?

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SUMMARY

The discussion focuses on calculating the speed of a sprinter's image as he runs away from a camera with a 160-mm focal length lens at a speed of 5.5 m/s. The key equation involved is the lens formula, 1/f = (1/d_object) + (1/d_image), which relates the object distance and image distance. Participants emphasize the need to differentiate this equation to find the rate of change of the image distance, which is crucial for solving the problem. The correct approach involves understanding related rates in calculus to connect the sprinter's speed to the image speed.

PREREQUISITES
  • Understanding of the lens formula in optics
  • Basic knowledge of related rates in calculus
  • Familiarity with unit conversions (e.g., m/s to mm/s)
  • Concept of focal length in photography
NEXT STEPS
  • Study the differentiation of the lens formula for related rates problems
  • Learn about unit conversions between meters and millimeters
  • Explore the concept of image distance in optics
  • Review calculus applications in physics, particularly related rates
USEFUL FOR

Students studying physics, particularly those interested in optics and calculus applications, as well as photographers looking to understand the mechanics of image capture at varying distances.

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Firsts of this is not my problem I don't even take physics but it is my girlfriends. She doesn't know how to get the answer an neither do I. I took some physics but not enough for this.

1. Homework Statement

A sports photographer has a 160-mm-focal-length lens on his camera. The photographer wants to photograph a sprinter running straight away from him at 5.5 m/s .

QUESTION:
What is the speed (in mm/s) of the sprinter's image at the instant the sprinter is 12 m in front of the lens?

Homework Equations

The Attempt at a Solution


I did some research online and through the book and I understand what it is asking. I visualize the problem in my head but I can't find the correct equations for this.

We just need some guidance on where to look or what equations to use and maybe how to use them.

Thank you physics forums community.
 
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Any relevant equations you can supply that might pertain to this problem?
 
Unfortunately at the moment I do not. Currently on khan academy after the Optics section maybe I will.
I apologize
 
vela said:
Any relevant equations you can supply that might pertain to this problem?

The only equation i came out with was

1/f = (1/d object) + (1d image)
 
Good. You're interested in the rate of change of ##d_\text{obj}## and ##d_\text{img}##, so you need to differentiate that equation. This is like a related-rates problem in calculus.
 
vela said:
Good. You're interested in the rate of change of ##d_\text{obj}## and ##d_\text{img}##, so you need to differentiate that equation. This is like a related-rates problem in calculus.

so i got

1/f = 1/object + 1/ image = 1/160 = 1/12000-mm + 1/image =(37/6000)-mm is the image distance
so far am i correct?
 
Not quite. You found ##\frac{1}{d_\text{img}} = \frac{37}{6000\text{ mm}}##. You have to take the reciprocal of both sides to find ##d_\text{img}##.
 
vela said:
Not quite. You found ##\frac{1}{d_\text{img}} = \frac{37}{6000\text{ mm}}##. You have to take the reciprocal of both sides to find ##d_\text{img}##.
Yea i noticed it later. so ended up with . (6000/37) - mm which comes out to 162 mm.
so its 162mm/s
 
No, you found the image distance. If the sprinter was stopped at a distance of 12.0 m, the image distance would remain at 162 mm. What you want to find is the rate of change of the image distance, which is going to be related to the speed of the sprinter. (You might have noticed you didn't use that piece of information yet.)
 

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