Question

two straight tracks AOB and COD meet each other at right angles at point o. A person walking at a
speed of 5 km/h along AOB is at the crossing O at 12 o'clock noon. Another person walking at the same
speed along COD reaches the crossing O at 1:30 PM. If the time at which the distance between them is
least is 12:T PM, then find T.
ita volocity vector​

Answer 1

Answer:

If the time at which the distance between them is

least is 12:T PM, then the value of T is 45.

Explanation:

Let T=Time

Distance of first person from 'O' who is walking along AOB

d1=[5×1.5]+vT  

   =7.5+5T

Distance of second person from 'O' who is walking alob COD

d2=vT  

 =5T

Distance between the two persons:

x=d1^2+d2^2  

=[7.5+5T]^2+[5T]^2

dx/dT=2[7.5+5T] [5]+2[5T][5]        

     =75+50T+50T        

     =75+100T

For the least  value,

dx/dT=0

75+100t=0

T=−0.75 hours

   =−0.75×60  

    =−45 minutes

Therefore 45 minutes is the answer.