Calculus

posted by .

A man 5.50 ft tall approaches a street light 18.0 ft above the ground at a rate of 4.0 ft/s. at what rate is the end of the man's shadow moving when he is 9.0 ft from the base of the light?

  • Calculus -

    Make a sketch.
    Let the distance between the man and the post be x ft
    let the length of his shadow be y ft
    by similar triangles:
    5.5/y = 18/(x+y)
    18y = 5.5x + 5.5y
    12.5y = 5.5x
    12.5dy/dt = 5.5dx/dt
    given: dx/dt = 4 ft/s

    then dy/dt = 5.5/12.5 or .44 ft/s

    So the shadow is lengthening at .44 ft/s
    and the shadow is moving at 4+.44 or 4.44 ft/sec

    (The end of the shadow is both lengthening and being moved along by the movement of the man.
    Similar to somebody walking in a moving train.
    Suppose a train is going at 60 mph, but somebody is walking inside the train at 4 mph in the same direction as the train. To an observer at a crossing, the person would be moving at 64 mph )

  • Calculus -

    wrong answer

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Shadow Length A man 6 feet tall walks at a rate of 3 ft per second away from a light that is 16 ft above the ground (see figure). When he is 11 ft from the base of the light find the following. (a) The rate the tip of the shadow is …
  2. Calculus

    A street light is hung 18 ft. above street level. A 6-foot tall man standing directly under the light walks away at a rate of 3 ft/sec. How fast is the tip of the man's shadow moving?
  3. calculus

    My problem is that a stft above the sidewalk. a man 6ft tall walks away from the light at the rate of 3ft/sec. at what rate is his tip of shadow moving
  4. Calculus- rates

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

    A man 5.00 ft tall approaches a street light 17.0ft above the ground at the rate of 4.00 ft/s. How fast is the end of the man's shadow moving when he is 9.0 ft from the base of the light?
  8. Calculas

    A man 6.5 ft tall approaches a street light 17.0ft above the ground at the rate of 8.00 ft/s. How fast is the end of the man's shadow moving when he is 5.0 ft from the base of the light?
  9. calculus

    A 5.5 foot tall woman walks at 6ft/s torward a street light that is 16.5 ft above the ground. what is the rate of change of the length of her shadow when she is 14ft from the street light?
  10. 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?

More Similar Questions