Question
Two particles A and B move with constant velocities v_{1} and v_{2} along two mutually perpendicular straight lines towards the intersection point O. At moment t = 0 the particle were located at distances l_{1} and l_{2} from O respectively. Find the time when they are nearest and also this shortest distance.

None of these



medium
Solution
As shown in Fig. in time t, A will move a distance v_{1}t while B, v_{2}t; so after time t the distance A and B from O will be (l_{1} – v_{1}t) and (l_{2} – v_{2}t) respectively. So the distance between them L at time t will be given by
Differentiating Eqn. (1) with respect to time,
Now for L to be minimum (dL/dt) = 0;
Substituting this value of t from Eqn. (2) in (1) and simplifying, we get
Eqns. (2) and (3) are the desired results.
SIMILAR QUESTIONS
A particle moves along a straight line such that its displacement at any timet is given by s = (t^{3} + 6t^{2} + 3t + 4)m. What is the velocity of the particle when its acceleration is zero?
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