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Solve it

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Asked by hariom2083 19th July 2018, 6:38 PM
Answered by Expert
Answer:
Let particle-A is projected with intial velocity v and the projection angle is θ.
Let particle-B is projected with intial velocity v and the projection angle is 2θ. (θ<45)
 
Let after time t, velocities of both the particles are parallel to each other.
 
In projectile motion, tangent of angle made by the velocity of particle  with horizontal at a given instant is
the ratio of y-component of velocity to the x-component of velocity.
 
hence if the above mentioned ratio is same for both the particle, then their velocities are parallel to each other.
 
If the ratio of y-component velocity to x-component velocity at the time t is equated
for both the particle, then we get the following equation.
 
begin mathsize 12px style fraction numerator v space sin theta space minus space g space t over denominator v space cos theta end fraction space equals space fraction numerator begin display style v space sin 2 theta space minus space g space t end style over denominator begin display style v space cos 2 theta end style end fraction space.................. left parenthesis 1 right parenthesis end style
begin mathsize 12px style tan theta space minus fraction numerator g space t over denominator v end fraction space s e c theta space equals space tan 2 theta space minus fraction numerator g space t over denominator v end fraction space s e c 2 theta
fraction numerator g space t over denominator v end fraction open curly brackets s e c space 2 theta space minus space s e c space theta close curly brackets space equals space tan space 2 theta space minus space tan space theta
end style
I leave it as a trignometry exercise to the student to get the answer, begin mathsize 12px style t space equals space v over g space cos theta over 2 space cos e c fraction numerator 3 theta over denominator 2 end fraction end style
Answered by Expert 19th July 2018, 9:50 PM
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