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Asked by rbhatt16 10th July 2018, 11:40 PM
Answered by 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 Expert 17th July 2018, 10:39 PM
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