Particles P and Q are in motion. Particle P is moving with a veloctiy of 10root3 km/hr towards west, and particle Q is moving with a velocity of 10 km /hr towards north. If the initial distance between the two particles is 20 km, then calcate the shortest distance between the particles.??

Dear Student,

Velocity of the P is 103 km/h. 
​Velocity of Q is 10 km/h. 

Let t be the time passed distance covered by P = 103t and distance covered by Q = 10t 

Distance (S) between the ships is given by

s=20-10t2+103t2     .....(i)For s to be minimum, dsdt=0dsdt=1220-10t2+103t21/2220-10t(-10)+2103t103=0-2020-10t+600t=0t=12 h
Putting this value in equation (i), we get 
smin=20-1022+10322   smin=129.90 km

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