IIT JEE , AIEEE Forum - Physics , Mechanics

kirtana

this sum is 1.13 of irodov

point A moves uniformly with velocity v so that the vector v is continuously aimed at point "B" which i turn moves rectilinearly and uniformly with velocity u<v. at the initil moment of time v is perpendicular to u and the points are sperated by a distance l. how soon will yhe points converge??

answer is vl/(v2 - u2)

puneet1622

Try to solve for by visualizing the situation at any general angle and then see if the question can be done. The fact that A will move l distance in vertical direction before catching A might may be useful. What trick have u used ??

Admin

Dear kirtana,

puneet1622 has pointed to the right approach. try solving using this approach and post so that we can guide you through the exact issues. this will help you grasp the concept better

kirtana

hello thanx for the solution

i tried to solve by resolving the velocites in the two directions

i took a general angle between the two particles as

in the horizontal dirction

distance travelled by
B in time t is ut ...........................( if t is time after wich they meet)

thefore for point A

_{[ 0]}

^{[t ]} v cos

dt = ut

hence

_{[ 0]}

^{[ t]} cos

dt = ut/v

in the vertical direction

relative velocity is v - u cos

l =

_{[ 0]}

^{[ t]} v - u cos

after solving and then substituing

we get

l = vt - u (ut/v)

then

t = lv / (v2 - u2)

is the method right??

puneet1622

in the vertical direction

relative velocity is v - u cos

......... how is this true ??? cud not understand this !!!

kirtana

if u take any general angle

and extend the line joining A and B ull get the angle between the line and the motion of B as

so the motion of B along that line is u cos

puneet1622

Sorry I do not agree with this soultion ........ this seems to be incorrect !!

kirtana

if u try to draw the diagram it works i think
i cant think of ne thing else...
cud u plz suggest some other approach then??

puneet1622

well the solution i am getting is not matching the answer you have put .. so i am not sure about the approach i used .. but definitely what u have used is wrong !!

vikalp

hey hey kirtana and puneet ,

the solution that kirtana has provided is alright no problems with that , the only thing that she has written incorrectly is that " relative velocity in vertical direction " ....because its not the relative velocity in vertical direction , its actually just relative velocity and its direction changes every second . so we write the equation as

integral of ( relative velocity between two) = relative displacement between two

which is the fundamental equation of kinematics ...............

and the other equation is quite straightforward.............

matrix

Point A has to move two dimensionally. One vertically and second horizontally. Consider that A takes a time ' T ' to catch up with B. Let B be moving horizontally . And the vertical distance between A and B is l.

Therefore we have two equations in X and Y directions. At first in Y direction we have ( vertically) for A and B

₀

^T ( v - u cos

) dt = l -------- ( 1)

where '

' is the angle made by the line joining A and B at any time ' t' with respect to the horizontal.

Now horizontally for A and B

₀

^T v cos

dt = uT -------- (2)

Solving 1 and 2 we get the required result.

gopi_mith

Guys and gals,don't do irodov else
'you know not what may fall upon you'

kirtana

hey, commonn

irodov's a great book.. it helps u to think a lot... even my classes professor( an iitian) recommends it..

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