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Physics-

General

Easy

Question

The equation of trajectory of a projectile is $y equals 10 x minus open parentheses fraction numerator 5 over denominator 9 end fraction close parentheses x to the power of 2 end exponent.$ if we assume $g equals 10 m s to the power of negative 2 end exponent$ , the range of projectile (in metre) is

36
24
18
9

The correct answer is: 18

Equation of projectile
$y equals x minus open parentheses fraction numerator 5 over denominator 9 end fraction close parentheses x to the power of 2 end exponent$
Standard equation
$y equals x tan invisible function application theta minus fraction numerator g over denominator 2 u to the power of 2 end exponent c o s to the power of 2 end exponent theta end fraction bullet x to the power of 2 end exponent$
$O n blank c o m p a r i n g comma blank w e blank g e t$
$tan invisible function application theta equals 10$
$a n d blank fraction numerator g over denominator 2 u to the power of 2 end exponent c o s to the power of 2 end exponent theta end fraction equals fraction numerator 5 over denominator 9 end fraction$
$o r blank 10 u to the power of 2 end exponent c o s to the power of 2 end exponent theta equals 9 g$
$g equals 10 blank m s to the power of negative 2 end exponent$
$therefore blank u to the power of 2 end exponent c o s to the power of 2 end exponent theta equals 9$
$r a n g e blank o f blank p r o j e c t i c l e blank R equals fraction numerator 2 u to the power of 2 end exponent tan invisible function application theta bullet cos invisible function application theta over denominator g end fraction$
$equals fraction numerator 2 u to the power of 2 end exponent tan invisible function application theta bullet cos invisible function application theta over denominator g end fraction$
$left parenthesis because sin invisible function application theta equals tan invisible function application theta bullet cos invisible function application theta right parenthesis$
$fraction numerator 2 left parenthesis u to the power of 2 end exponent c o s to the power of 2 end exponent theta right parenthesis bullet tan invisible function application theta over denominator g end fraction$
$equals fraction numerator 2 cross times 9 cross times 10 over denominator 10 end fraction equals 18 blank m$

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