Three particles starts from origin at tha same time . One along positive x-axis with velocity v1 second along positive y axis with velocity v2 and third along the line y=x in such a speed that all three particles will always remain in a straight line , what is the velocity of third particle.
Three particles starts from origin at tha same time . One along positive x-axis with velocity v1 second along positive y axis with velocity v2 and third along the line y=x in such a speed that all three particles will always remain in a straight line , what is the velocity of third particle.
Let us consider particles starts from origin, positive x and positive y are taken east and north respectively. The position of first particle at time t is (v1t,0)
The position of second particle at time t is (0,v2t)
The equation of line joining these two positions
y = [(v2t - 0) / (0-v1t)] (x-v1t) + 0
y = -(v2/v1)(x-v1t)
=> y = -(v2/v1)x + v2t.......(1)
Equation of the path of third particle
y = x .......(2)
from 1 & 2 we get,
x = y = [v1v2/(v1+v2)]t
distance of this point from origin d
= √2 [v1v2/(v1+v2)]t
If third particle attains such distance in time t then the will be lie on a line
therefore
v3 t = d
v3 =
√2 [v1v2/(v1+v2)
Let us consider particles starts from origin, positive x and positive y are taken east and north respectively.
The position of first particle at time t is (v1t,0)
The position of second particle at time t is (0,v2t)
The equation of line joining these two positions
y = [(v2t - 0) / (0-v1t)] (x-v1t) + 0
y = -(v2/v1)(x-v1t)
=> y = -(v2/v1)x + v2t.......(1)
Equation of the path of third particle
y = x .......(2)
from 1 & 2 we get,
x = y = [v1v2/(v1+v2)]t
distance of this point from origin d
= √2 [v1v2/(v1+v2)]t
If third particle attains such distance in time t then the will be lie on a line
therefore
v3 t = d
v3 =
√2 [v1v2/(v1+v2)
