differential calculus

a man 6 ft tall is walking toward a building at the rate of 4 ft/sec. if there is a light on the ground 40 ft from the building, how fast is the man's shadow on the building growing shorter when he is 30 ft from the building?

  1. 0
asked by jordan
  1. Using similar triangles, if the man is x from the light, and his shadow is h tall,

    h/40 = 6/x
    1/40 dh/dt = -6/x^2 dx/dt
    So, when the man is 10 ft from the light,

    1/40 dh/dt = -6/100 * 4
    dh/dt = -9.6 ft/s

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    A man 1.69 meters tall is walking towards a building at the rate of 1.5 meters per second. If there is a light on the ground 15 meter from the building, how fast is the man's shadow on the building growing shorter when he is 5
  2. math- bc calc

    a building is 36 ft tall. A pulley is attached to the top of the building. A rope is looped through the pulley. One end of the rope is attached to the lantern that hangs vertically parallel to the side of the building. The rope
  3. Differential calculus

    A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward the building at the rate of 5 ft/sec. Find the rate at which the length of his shadow is changing when he is 15 ft from the
  4. math

    A man who is 1.6 m tall is walking on the road at a constant speed of 1 m/s. There is (only) one lamp placed 3.2 m above the road. At a specific moment the man was just under the lamp. What will be the rate at which the length of
  5. math

    A man who is 1.6 m tall is walking on the road at a constant speed of 1 m/s. There is (only) one lamp placed 3.2 m above the road. At a specific moment the man was just under the lamp. What will be the rate at which the length of
  6. Calculus

    A light is hung 15 ft above a straight horizontal path. If a man 6 ft tall is walking away from the light at the rate of 5 ft/sec, how fast is his shadow lengthening and at what rate is the tip of the man’s shadow moving?
  7. Calculus

    A man is 6ft tall and is walking at night straight toward a lighted street lamp at a rate of 5 ft/sec. If the lamp is 20 ft above the ground, find the rate at which the length of his shadow is changing.
  8. 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?
  9. AP Calculus AB

    Hello! I'm having trouble with this related rates problem: A 5ft tall person is walking away from a 16ft tall lamppost at a rate of (2/x) ft/sec, where x is the distance from the person to the lamppost. Assume the scenario can be
  10. physics

    A man 2 m tall is walking away from a lamppost which is 6m tall at a rate of 2 m/s. Find the rate of change of a)the tip of the shadow b) the length of his shadow

More Similar Questions