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[ghostdet]

Two straight roads meet at an angle of 60 degrees. A starts from the intersection and travels along one road at 40 km/hr. One hour later B starts from the intersection and travels along the other road at 50 km/hr. At what rate is the distance between them changing three hours after A starts?'

 

[cineti970128]

You have to use consine rule to find the distance in terms of t and differentiate that

 

[cineti970128]

I will post the answer soon

 

[cineti970128]

Think about the time frame since B starts an hour after A
Think A starts 40km from the origin with speed 40km/h
And B starts from the origin with speed 50km/h

Hence
D (A)= 40 + 40t
D (B) = 50t

Hence using the cosine rule

D^2 = D (A)^2 +D(B)^2 - 2D(A)×D(B)×cos (60)

= 1600 + 3200t + 1600t^2 + 2500t^2 - 2000t - 2000t^2
=etc

Then differentiating using chain rule
Substitute t=2 note that t is not 3

Then all gg