JEE Plances Class Answered

Ques 28

Asked by rbhatt16 | 10 Jul, 2018, 23:40: PM

Expert Answer

A takes m second more than B to acquire same speed.

hence we have, v = f×(m+t) = f ' × t ................(1)

from eqn.(1), we get,

begin mathsize 12px style m space equals space fraction numerator open parentheses f apostrophe space minus space f close parentheses over denominator f end fraction cross times t end style

...................(2)

A moves n units more than B to acquire same speed

hence we have,

begin mathsize 12px style 1 half f cross times open parentheses t plus m close parentheses squared space equals space 1 half f apostrophe cross times t squared space plus space n space end style

...............(3)

from eqn.(2), we can write,

begin mathsize 12px style t plus m space equals space open parentheses fraction numerator f apostrophe space minus space f over denominator f end fraction close parentheses cross times t space plus space t space equals space fraction numerator f apostrophe over denominator f end fraction cross times t space end style

.................(4)

substitute for (t+m) from eqn.(4) in eqn.(3), we get,

begin mathsize 12px style 1 half f apostrophe cross times t squared space plus space n space equals space 1 half fraction numerator f apostrophe squared over denominator f end fraction t squared space n space equals space 1 half fraction numerator f apostrophe over denominator f end fraction open parentheses f apostrophe space minus space f close parentheses cross times t squared space.................... left parenthesis 5 right parenthesis end style

if we substitute t from eqn.(2) in eqn.(5), we have,

begin mathsize 12px style n space equals space fraction numerator f space f apostrophe over denominator open parentheses f apostrophe space minus space f close parentheses end fraction m squared over 2 space space space o r space space space space open parentheses f apostrophe space minus space f close parentheses cross times n space equals space 1 half f space f apostrophe space m squared end style

Answered by Thiyagarajan K | 17 Jul, 2018, 22:39: PM

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