A man starts walking north at 2ft/s from a point P. Twenty-five seconds later a woman starts walking south at 3ft/s from a point 400ft due east of P. At what rate are the people moving apart 50 seconds after the woman starts walking? Do not include units in your answer.

  1. 👍 0
  2. 👎 0
  3. 👁 195
  1. Man starts north at t = 0 from origin
    Woman starts south at t = 25 from (400,0)
    where are they at t = 75?
    man 2*75 = 150 so at (0,150)
    woman 3*50 = 150 so at (400,-150)
    distance apart is hypotenuse of triangle with legs 300 and 400 so 500 ft
    How fast is this changing?
    The north south difference is changing at 2+3 = 5 ft/s
    The East west distance is not changing at all
    start new t now at 0
    N-S distance = 300 + 5 t
    E-W distance = 400
    h is hypotenuse, the distance
    h^2 = 400^2 + (300+5t)^2
    2 h dh = 0 + 2 (300+5t)(5)dt
    h dh = 5(300+5t) dt
    at h = 500 and t = 0 this is
    500 dh = 5(300) dt
    dh/dt = .01(300) = 3

    1. 👍 0
    2. 👎 0
  2. let the times passed since the woman started walking be t seconds
    make a diagram
    distance covered by man = 50 + 2t
    distance covered by woman = 3t
    let the distance between them be D
    I see a right-angled triangle with hypotenuse D,
    the vertical line as (50+2t+3t)
    and the horizontal as 400

    D^2 = (5t+50)^2 + 400^2
    2D dD/dt = 2(5t+50)(5) + 0
    dD/dt = 5(5t+50)/D

    when t = 50,
    D^2 = 300^2+400^2
    D = 500

    dD/dt = 5(300)500 = 3

    1. 👍 0
    2. 👎 0
  3. thank you very much

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. English

    1. Which of the following sentences uses capitalization CORRECTLY? (1 point) A.) You can find the complete list of Senators online. B.) Have you ever read The History of Tom Jones, a Foundling? C.)The Maryland Blue Crabs have

    asked by Cassie on April 15, 2014
  2. physics

    A toy plane p starts flying from point A along a straight horizontal line 20 m above ground level starting with zero initial velocity and acceleration 2 m /s² as shown. At the same instant, a man P throws a ball vertically

    asked by karan on July 15, 2014
  3. Physics

    A man at point A directs his rowboat due north toward point B, straight across a river of width 100 m. The river current is due east. The man starts across, rowing steadily at 2.50 m/s and reaches the other side of the river at

    asked by Marissa on February 2, 2014
  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?

    asked by Sandra on May 2, 2016
  5. Math

    The dealer sold a car to a man and made a profit of 15%.the man then sold it to a woman for one hundred twenty thousand,one hundred and seventy five at a loss of much did he buy the car?

    asked by Anonymous on November 4, 2019
  1. diffirential calculus

    a woman 6ft tall walks away from a light 10ft above the ground. if her shadow lengthens at the rate of 2ft/sec. how fast is she walking?

    asked by kait on September 25, 2011
  2. Chemistry

    A woman expends 96 kJ of energy in walking a kilometer. The energy is supplied by the metabolic breakdown of food intake and has a 35 % efficiency. If the woman drives a car over the same distance, how much energy is used if the

    asked by James on March 27, 2015
  3. Physics


    asked by Anonymous on June 19, 2019

    Two skaters, a man and a woman, are standing on ice. Neglect any friction between the skate blades and the ice. The mass of the man is 88 kg, and the mass of the woman is 58 kg. The woman pushes on the man with a force of 56 N due

    asked by Anonymous on October 4, 2015
  5. Physics

    A golfer rides in a golf cart at an average speed of 3.10 m/s for 21.0 s. She then gets out of the cart and starts walking at an average speed of 1.60 m/s. For how long (in seconds) must she walk if her average speed for the

    asked by Kristina on October 2, 2009
  6. trigonometry

    A river is 2000 ft wide and flowing at 6 mph from north to south. A woman in a canoe starts on the eastern shore and heads west at her normal paddling speed of 2 mph. In what direction (measured clockwise from north) must she aim

    asked by brittney on January 8, 2012

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