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A light is on the top of a 12 ft tall pole and a 5’6’’ tall person is walking away from the pole at a rate of 2 ft/sec At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole? At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole? please give all solutions

Sagot :

Part a: the rate at which the shadow's tip moves away from the pole while the subject is 25 feet distant is 48/13 ft/sec.

Part b: the speed of the shadow from the speed of the man is 22/13 ft/sec.

Explain the term rate of change?

  • Rate of Change: How quickly a parameter changes over a predetermined amount of time.
  • It is frequently used while discussing momentum and is typically expressed as a proportion of one variable's change to another's corresponding change.

A 5 feet 6 inch tall individual is going away from a 12 foot tall pole with a light on top at a 2 foot per second pace.

A) the speed at which the shadow's tip moves away from the pole while the subject is 25 feet distant;

Similar triangles allow us to say:

12/L = 55/(L - x)

Simpllifying,

12(l - x) = 5.5l

12l - 12x = 5.5l

6.5l = 12x

x = (6.5/12)l

Differentiate with respect to time;

dx/dt = (6.5/12)dl/dt or

dl/dt = (12/6.5)(dx/dt)

As, dx/dt = 2

dl/dt = (12/6.5)(2)

dl/dt = 24/6.5

dl/dt = 48/13 ft/sec

B: When a person is 25 feet from a pole, the point of the shadow travelling away from them at:

Subtract the speed of the shadow from the speed of the man.

Therefore,

48/13 - 2 = 22/13 ft/sec.

Thus, the speed of shadow from the speed of the man is 22/13 ft/sec.

To know more about the rate of change, here

https://brainly.com/question/8728504

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