Posted by Please Help! on Friday, October 1, 2010 at 3:33pm.
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 the distance between them is 300 m? (Round to 2 decimal places.
My teacher tried helping me with this problem and only confused me more. I drew a diagram. I used the formula c^2=a^2+b^22abcosC. Right now I have 2L(dL/dt)=2(150)(300)sin(angle)(dangle/dt) I think (dangle/dt) is 7/150. This would give you (solving for dL/dt:
(dL/dt)= (45000sin(angle)(7/100))/300
HELP!!!!!

College Calculus 1  MathMate, Friday, October 1, 2010 at 10:28pm
I suggest the following approach.
Let the friend (outside of the tracks) be at the origin.
Express the x and y coordinates of the runner in terms of t, for example,
X(t)=rcos(st/r)+d
Y(t)=rsin(st/r)
s=speed in m/s
r=radius
d=given distance
Express the distance between the two persons in terms of t:
L(t)=√(X(t)²+Y(t)²)
Differentiate L(t) with respect to t, which gives L'(t), the rate of change of distance as a function of t.
Finally, find the times at which the two persons are 300m apart, namely, solve for t at which
L(t)=300.
The answers are t1=39 and t2=96 seconds approx.
L'(t1) and L'(t2) are the required answers.
I get about ±6.8 m/s, which is reasonable considering that the runner runs at 7m/s and the points in question are not far from the points of tangency (where L'(t) should give ±7m/s).

College Calculus 1  Shayne, Monday, October 4, 2010 at 7:56pm
I have no fricken clue. That's why I fricken hatee MATH. LIKE HOLY FRICK! WHY THE FRICK DO WE HAVE TO LEARN?

College Calculus 1  Anonymous, Thursday, October 21, 2010 at 8:55pm
JEEZZZ,
dont understand."
it will be easier to learn by talking...
im confused with the signs hahaha!!!
Answer This Question
Related Questions
 Calculus  A runner sprints around a circular track of radius 150 m at a ...
 Related Rates Problem  A runner sprints around a circular track of radius 150 m...
 physics  A runner is moving at a constant speed of 8.00 m/s around a circular ...
 physics  A runner circles a track of radius 50 m in 50 s moving at a constant ...
 calculus  An athlete is running around a circular track of radius 50 meters at ...
 physics  A runner covers one lap of a circular track 40.0 m in diameter in 62.5...
 Physics  A runner runs around a circular track with a radius of 50m.if he runs ...
 physics  1.Moving with uniform acceleration a body covers 150m during 10sec so ...
 physics  Suppose runner A starts at the 0 degree mark on a circular track (...
 Physics  A runner with mass 100 kg jogs around a circular track with ...
More Related Questions