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TWO PARTICLES ARE MOVING ALONG TWO LONG STRAIGHT LINES IN THE SAME PLANE WITH SAME VEL=20cm/s.THE ANGLE BTW TWO LINES IS 60 AND THEIR INTERSECTION POINT IS O . AT A CERTAIN MOMENT , THE TWO PARTICLES ARE LOCATED AT DIS 4m AND 3m FROM O AND ARE MOVING TOWARDS O. SUBSEQUENTLY,THE SHORTEST DISTANCE BTW THEM IS?

TWO PARTICLES ARE MOVING ALONG TWO LONG STRAIGHT LINES IN THE SAME PLANE WITH SAME VEL=20cm/s.THE ANGLE BTW TWO LINES IS 60 AND THEIR INTERSECTION POINT IS O . AT A CERTAIN MOMENT , THE TWO PARTICLES ARE LOCATED AT DIS 4m AND 3m FROM O AND ARE MOVING TOWARDS O. SUBSEQUENTLY,THE SHORTEST DISTANCE BTW THEM IS?



 




 





 


 

Grade:11

1 Answers

rahul swain
40 Points
6 years ago
Let's say one particle is moving along the x-axis. 
(x1) = 300 - 20t 

The second particle is moving (initially) in quadrant 1. 
(x2) = (400 - 20t)cos60° 
(y2) = (400 - 20t)sin60° 

s² = [(300 - 20t) - (400 - 20t)cos60°]² + [(400 - 20t)sin60°]² 
s² = [(300 - 20t) - (1/2)(400 - 20t)]² + (3/4)(400 - 20t)² 
s² = (100 - 10t)² + (3/4)(400 - 20t)² 

d(s²)/dt = 2(-10)(100 - 10t) + 2(-20)(3/4)(400 - 20t) = 0 
(100 - 10t) + (3/2)(400 - 20t) = 0 
700 = 40t 
t = 35/2 

s² = (100 - 10(35/2))² + (3/4)(400 - 20(35/2))² 
s² = (-75)² + (3/4)(50)² 
s² = 
s² = 25²[3² + 3] 
s² = 25²(12) 
s = 50sqrt(3)

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