Question

Three particles start from origin at the same time, one with a velocity along positive x-axis, the second with a velocity along negative y-axis. Find the velocity of the third particle along line so that the three particles should always lie in a straight line

Answer 1

Answer:

Distance on y axis is V2, on x axis is V1, if we calculate the distance of 3rd partcle along line y=x just after 1 second we will get its velocity.

In order to do so join particles P2 and P1 by a line and find its intercept on the line y=x

Line joining P2 and P1 : y - V2 = (- V2/V1 ) x -equation 1

( Distance on y axis is V2, on x axis is V1 so slope will be -V2/V1)

Now find the point of intersection btw y = x and equation 1

you will get x = V1 V2 / (V1 + V2) and y same as x

which will be your intersection point [V1 V2 / (V1 + V2) , V1 V2 / (V1 + V2)]

So the distance it travels in 1 second and hence the velocity will be sqrt(2) times x (as y = x)

i.e

sqrt(2 ) V1 V2 / (V1 + V2)