math

Boris and Stella are running on a circular track which has a
radius of 300 meters. They start running at the same time.
Boris starts at the northernmost point of the track, and
Stella starts at the easternmost point. Boris runs clockwise.
Stella runs counterclockwise, and she runs twice as fast as
Boris runs. They pass each other for the first time after 85
seconds. How far apart are Boris and Stella when they
have been running for 800 seconds?

  1. 👍 0
  2. 👎 0
  3. 👁 87
  1. They are 1/4 of a circle apart to begin.
    Boris runs 1/12 of a circle and Stella runs 1/6 of a circle in 85 seconds.
    So, Boris's angular speed is ω = 2π/85 and Stella's speed is 4π/85
    So, at time t,
    Boris's location is (300 sin 2π/85 * 800, 300 cos 2π/85 * 300)
    Stella's location is (300 cos 4π/85 * 800, 300 sin 4π/85 * 300)
    So just use the distance formula to get the answer.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. mathematics

    A circular race track is being built. The outsidediameter of the track is 200 feet, and the inside diameter is 180 feet. If two runners run around the track once, with one of them running on the outside edge of the track, while

  2. Physics

    A car travels on a circular banked track of radius 300 m and having a banked angle of 22. What is the minimum time for one lap of the track if the car does not rely on friction to hold it on to the track?

  3. Math

    Lee is running around the perimeter of a circular track at a rate of 10 ft/sec. The track has a radius of 100 yards. After 10 seconds, Lee turns and runs along a radial line to the center of the circle. Once he reaches the center,

  4. math

    There is a diagram of a running track. The track is made up of two straights and two semicircles. The radius of each semicircle is 35 meters. The length of the outer perimeter of the entire running track is 400 meters. Find the

  1. math

    Running at an average rate of 4 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 2 meters per second. The total time for the sprint and the jog back

  2. College Calculus 1

    A runner sprints around a circular track of radius 150 m at a constant speed of 7 m/s. The runner's friend is standing at a distance 300 m from the center of the track. How fast is the distance between the friends changing when

  3. Physics

    Consider a circular track with a radius of 200 meters. A runner starts on the east side and runs around the track to a point diametrically opposite her starting point. -What is the magnitude of her displacement? 400m -She then

  4. Math

    A running track is designed with two semicircular ends and two parallel straightaways. If the inner perimeter of the track is to be exactly 400 meters, what are reasonable dimensions for the radius and straightaway of the track?

  1. physic

    A race car travels 950 km around a circular sprint track of radius 1.343 km. How many times did it go around the track?

  2. Math

    A running track consists of two straight sections with semi-circular ends. If the straight sections measure 100 metres and one compete lap on the inside of the track measures 1/2 k, what is the distance x between the two

  3. Physics

    A circular track has several concentric rings where people can run at their leisure. Phil runs on the outermost track with radius rP while Annie runs on an inner track with radius rA = 0.90 rP. The runners start side by side,

  4. PHysics!!

    Starting from rest at a height equal to the radius of the circular track, a block of mass 25 kg slides down a quarter circular track under the influence of gravity with friction present (of coefficient μ). The radius of the track

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