A runner sprints around a circular track of radius 100m at a constant speed of 7 m/s. The runner’s friend is standing at a distance 200m from the center of the track. How fast is the distance between the friends changing when the distance between them is 200m?
2 answers
http://www2.sunysuffolk.edu/pestiej/related_rates.pdf
An object is moving along a circular path of radius r. (5 marks)
(a) Show that its velocity vector is perpendicular to the radial rays at any moment. This confirms that the velocity vector is tangent to the path, as it should be.
(b) Show that its acceleration vector is perpendicular to its velocity vector if the object rotates with a fixed speed. This confirms that the acceleration vector will be parallel to the radial ray at any moment.
Hint: Use the fact that every two vectors u = (ux,uy) and v = (vx,vy) are perpendicular exactly if uxvx + uyvy = 0.
(a) Show that its velocity vector is perpendicular to the radial rays at any moment. This confirms that the velocity vector is tangent to the path, as it should be.
(b) Show that its acceleration vector is perpendicular to its velocity vector if the object rotates with a fixed speed. This confirms that the acceleration vector will be parallel to the radial ray at any moment.
Hint: Use the fact that every two vectors u = (ux,uy) and v = (vx,vy) are perpendicular exactly if uxvx + uyvy = 0.
1 answer