pls prove that

Asked by psreeramasetty | 19th May, 2020, 07:43: AM

Expert Answer:

Let u be the initial velocity of the bullet. 
Bullet loses 1/n of the velocity while penetrating distance x in target
To find: - further distance travelled by bullet before coming to rest
Solution: - 
 
W e space k n o w comma space t h i r d space e q u a t i o n space o f space m o t i o n space i s space
v squared space minus space u squared space equals space 2 a s space... left parenthesis 1 right parenthesis
F o r space f i n d i n g space t h e space d i s tan c e space c o v e r e d space b y space t h e space b u l l e t space b e f o r e space c o m i n g space t o space r e s t space
w e space m u s t space k n o w space t h e space a c c e l e r a t i o n space o f space a space b u l l e t space
W h e n space b u l l e t space t r a v e l s space d i s tan c e space apostrophe x apostrophe space
t h e space v space equals space u over n space... left parenthesis 2 right parenthesis
T h u s comma space
a space equals fraction numerator open parentheses space begin display style u over n end style close parentheses squared minus u squared over denominator 2 x end fraction equals space fraction numerator u squared minus n squared u squared over denominator 2 x n squared end fraction
therefore space a space equals space space minus space open square brackets fraction numerator space u squared left parenthesis n squared minus space 1 right parenthesis over denominator 2 x n squared end fraction close square brackets space... space left parenthesis 2 right parenthesis space space... left parenthesis n e g a t i v e space s i g n space i n d i c a t e s space r e t a r d a t i o n right parenthesis
bold italic L bold italic e bold italic t bold space bold italic y bold space bold italic b bold italic e bold space bold italic t bold italic h bold italic e bold space bold italic d bold italic i bold italic s bold italic t bold italic a bold italic n bold italic c bold italic e bold space bold italic t bold italic h bold italic r bold italic o bold italic u bold italic g bold italic h bold space bold italic w bold italic h bold italic i bold italic c bold italic h bold space bold italic i bold italic t bold space bold italic w bold italic i bold italic l bold italic l bold space bold italic p bold italic e bold italic n bold italic e bold italic t bold italic r bold italic a bold italic t bold italic e bold space bold italic f bold italic u bold italic r bold italic t bold italic h bold italic e bold italic r bold space bold italic a bold italic n bold italic d bold space bold italic c bold italic o bold italic m bold italic e bold italic s bold space bold italic t bold italic o bold space bold italic r bold italic e bold italic s bold italic t

T h e n space v space equals 0 comma space s equals y space a n d space u space equals u over n space... space left parenthesis 3 right parenthesis

N o w comma space
v squared minus u squared equals 2 a s space b e c o m e s
0 space minus space open parentheses space u over n close parentheses squared space equals space 2 cross times open parentheses space minus space open square brackets fraction numerator space u squared left parenthesis n squared minus space 1 right parenthesis over denominator 2 x n squared end fraction close square brackets close parentheses space space y space

therefore fraction numerator negative space open parentheses begin display style u squared over n squared end style close parentheses over denominator negative space open square brackets fraction numerator u squared left parenthesis n squared minus space 1 right parenthesis over denominator x n squared end fraction close square brackets end fraction space equals y

therefore space y space equals space space open parentheses u squared over n squared close parentheses cross times fraction numerator x n squared over denominator space u squared left parenthesis n squared minus space 1 right parenthesis end fraction space equals space fraction numerator x over denominator space u squared left parenthesis n squared minus space 1 right parenthesis end fraction

T h u s comma space d i s tan c e space t r a v e l l e d space f u r t h e r space b y space b u l l e t space b e f o r e space c o m i n g space t o space r e s t space i s space
therefore space y space equals fraction numerator x over denominator space u squared left parenthesis n squared minus space 1 right parenthesis end fraction space

Answered by Shiwani Sawant | 19th May, 2020, 02:21: PM