Physics-
General
Easy

Question

A projectile can have the same range R for two angles of projection. If T subscript 1 end subscript and blank T subscript 2 end subscriptbe the times of flights in the two cases, then the product of the two times of flights is directly proportional to

  1. fraction numerator 1 over denominator R to the power of 2 end exponent end fraction  
  2. fraction numerator 1 over denominator R end fraction  
  3. R  
  4. R to the power of 2 end exponent  

The correct answer is: R


    We know that range of projectile is same for complementary angles i e comma for theta blank a n d blank open parentheses 90 degree minus theta close parentheses.
    therefore blank T subscript 1 end subscript equals fraction numerator 2 u sin invisible function application theta over denominator g end fraction
    T subscript 2 end subscript equals fraction numerator 2 u sin invisible function application open parentheses 90 degree minus theta close parentheses over denominator g end fraction equals fraction numerator 2 u cos invisible function application theta over denominator g end fraction
    a n d blank R equals fraction numerator u to the power of 2 end exponent sin invisible function application theta over denominator g end fraction
    T h e r e f o r e comma blank T subscript 1 end subscript T subscript 2 end subscript equals fraction numerator 2 u sin invisible function application theta over denominator g end fraction cross times fraction numerator 2 u cos invisible function application theta over denominator g end fraction
    equals fraction numerator 2 u to the power of 2 end exponent left parenthesis 2 sin invisible function application theta cos invisible function application theta right parenthesis over denominator g to the power of 2 end exponent end fraction
    equals fraction numerator 2 u to the power of 2 end exponent left parenthesis 2 sin invisible function application theta right parenthesis over denominator g to the power of 2 end exponent end fraction equals fraction numerator 2 R over denominator g end fraction
    therefore blank T subscript 1 end subscript T subscript 2 end subscript proportional to R

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