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 base of the lamp post?

  1. 👍 0
  2. 👎 0
  3. 👁 1,025
  1. draw a diagram. using similar triangles, if the length of the shadow is x, and the distance to the lamp is y,

    x/6 = (x+y)/16
    16x = 6x + 6y
    10x = 6y
    x = 3/5 y

    since y is changing at -5ft/sec
    x is changing at -3ft/sec

    no matter where the man is.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    A man standing 9 feet from the base of a lamppost casts a shadow 6 feet long. If the man is 6 feet tall and walks away from the lamppost at a speed of 30 feet per minute, at what rate, in feet per minute, will his shadow lengthen?

  2. calculus

    A street light is at the top of a 15 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving (away from the woman) when she is 50 feet

  3. Calculus

    A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is her shadow lengthening when she is 30 ft from the base of the pole?

  4. algebra. help!

    Start from 110 feet away, a person on a bicycle rides towards a checkpoint and then passes it. The rider is travelling at a constant rate of 30 feet per second. The distance between the bicycle and the checkpoint is given by the

  1. Math

    Starting from 130 feet away, a person on a bicycle rides towards a checkpoint and then passes it. The rider is traveling as a constant rate of 25 feet per second. The distance between the bicycle and the checkpoint is given by the

  2. Bubbles

    starting from 105 feet away a person on a bicycle rides towards a checkpoint and then passes it. the rider is traveling at a constant rate of 35 feet per second. THe distance between the bicycle and the checkpoint is given by the

  3. Math

    a man 6ft tall walks at the rate of 5ft/sec toward a streetlight that is 16ft above the ground. At what rate is the length of his shadow changing when he is 10ft from the base of the light?

  4. Calculus

    A street light is at the top of a 19 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 feet from the base of the

  1. math

    A street light is at the top of a 11 ft. tall pole. A man 6.2 ft tall walks away from the pole with a speed of 4.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 31 feet from the pole?

  2. 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

  3. College Algebra

    A 6 ft tall man is standing 40 feet from the light post, if his shadow is 20 feet, determine the height of the lamp. Here I use simple ratios: 40ft + 20ft = 60ft 6/20 = h/60 Cross multiply both sides with 60: 6 (60)/20 = h 360/20

  4. Calculus-rates

    1.) A man 6 ft tall walks at a rate of 5 ft per sec. from a light that is 15 ft above the ground. At what rate is the top of his shadow changing? 2.) An airplane flies at an altitude of 5 miles toward a point directly over an

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