2 people start moving from the same point. One north at 3 m/s and one east at 4 m/s. At what rate is the distance between the two increasing 2 seconds later.

Question

Please show me how you got the answer.

Answer 1

First find instantaneous equation of distance between two people ay time t

 

distance traveled in time t in North direction = 3t

distance traveled in time t in East direction = 4t

 

Distance between these two points at time t = (9t² + 16t²)^1/2

 

Differentiate this expression to find rate of change w.r.t. time between two pints = d/dt((9t² + 16t²)^1/2)

 

= (18t + 32t)/2(9t² + 16t²)^1/2

 

Plug in t=2 to find rate of change of this distance at 2 seconds

 

= (36+64)/2(36+64)^1/2 = 5m/s

Answer 2

Dale,

 

      The simplest way to solve this is to write an equation for each person's position as a function of time

Pn(t)=3t

Pe(t)=4t     the subscripts n and e refer to north and east. Since the people are traveling in directions that are at right angles to each other the distance, D, between them is the hypotenuse of a triangle. 

 

D(t)=(Pn(t)² + Pe(t)²)^1/2 , substituting for Pe and Pn and  simplifying gives D(t)=5t so the rate of change dD/dt = 5m/s

 

This is the rate that the distance between the two is changing and is independent of t.

 

Jim