A person 150cm tall is walking away from a lamp post at the rate of 15 meter per minute. when the man is 2.5m from the lamp post, his shadow is 3m long. Find the rate at which the length of the shadow is increasing when he is 7m from the lamp post.

  1. 👍 0
  2. 👎 0
  3. 👁 490
  1. when the man is x from the pole, and his shadow is s,

    150/300 = h/(250+300)
    so, the pole's height is h=275 cm

    so, at any time,

    150/s = 275/(x+s)
    or, more easily manipulated,

    (x+s)/275 = s/150
    x/275 = s/330
    x = 5/6 s

    so, at any time
    dx/dt = 5/6 ds/dt

    since dx/dt = 15,
    ds/dt = 18 m/s regardless of the distance from the pole.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Language arts

    1)What does it mean when an author emphasizes evidence?(1 point) The author includes facts to support an opposite idea. The author makes an educated guess based on evidence. The author shares ideas supported by reasons. The author

  2. Algebra

    Walking Speed The avg. walking speed R of a person living in a city of population P in thousands is modeled by the function R(P)=0.37 times ln P + 0.05. where R is in feet per second. The populatin of Boston is 532,000, find the

  3. Bassick High School

    Vivian is walking to the hairdresser's at 1.3 m/s when she glances at her watch and realizes that she is going to be late for her appointment. Vivian gradually quickens her pace at a rate of 0.090 m/s2(squared) What is Vivians

  4. Calculus

    A light hangs 15 ft. directly above a straight walk on which a man 6 ft. tall is walking. How fast is the end of the man's shadow travelling when he is walking away from the light at a rate of 3 miles per hour?

  1. calc

    a man 6 feet tall is walking away from a lamp post at the rate of 60 feet per minute. when the person is 6 feet from the lamp post, his shadow is 12 feet long. find the rate at which the length of his shadow is increasing when he

  2. Applied Calculus

    For the average person that is still growing, the rate of change in weight W (in pounds) with respect to height h (in inches) is approximately dW/dh=0.0015h^2 pounds per inch. Suppose that the average person that is 60 inches tall

  3. math

    A man 6 feet tall walks at a rate of 5 feet/sec toward a street lamp that is 16 feet above the ground. At what rate is the tip ,of his shadow moving? At what rate is the length of his shadow changing when he is 10 feet from the

  4. math

    A man is 6ft tall is standing 10 feet from the base of a lamp post. The mans shadow has a lenght of 4ft . How tal is he lamp post

  1. math

    A boy of height 95 cm is walking away from base of a lamp post at a speed of 1.5 m/s.If the lamp post is 3.8 m above the ground, find the length of his shadow after 5 seconds.

  2. Math

    At the​ airport, Person A and Person B are walking at the same speed to catch their​ flight, but Person B decides to step onto the moving​ sidewalk, while Person A continues to walk on the stationary sidewalk. If the

  3. Math

    A 6 ft tall person walks away from a 10 ft lamppost at a constant rate of 5 ft/s. What is the rate (in ft/s) that the tip of the shadow moves away from the pole when the person is 10 ft away from the pole? I have drawn out the

  4. geometry

    a boy stands 1 meter away from a lamppost. he is 1.8 meters tall and casts a shadow 2 meters long in the light from the lamp. how tall is the lamppost?

You can view more similar questions or ask a new question.