Two students A and B are walking on straight roads that meet at right angles. Student A approaches that intersection from the west at 2 m/sec and student B moves south, away from the intersection, at 1 m/sec. At what rate is the angle changing when A is 10 m from the intersection and B is 20 m from the intersection? Express your answer in radians per second.


 

At what rate is the angle changing

 

In this problem all three variables (x,y, and z )are changing with respect to time.

x=20 and y=10

 = -1

 

= 2

 

tan(θ)=

 

Take Derivative:

 

tan(θ)=

 

 (θ)=

 

 

Substitute-

 

Solve:

 

 

 

 

 

This means that the angle is increasing as A get closer to the intersection and B gets father away from the intersection.