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Prove that the horizontal range is same ...

Prove that the horizontal range is same when angle of projection is (i) greater than ` 45^(@)` by certain value and (ii) less than ` 45^(@)` by the same value.

Text Solution

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Horizontal range for angular projection of a projectile is given by `R=(u^(2) sin 2theta)/(g)`
Case (i) When angle of projection, `theta=45^(@)+alpha, " let "R=R_(1)" (say), then "`
`R_(1)=((u^(2) sin 2(45^(@+alpha))/(g)=(u^(2))/(g) (90^(@)+2alpha)`
`=(u^(2) cos 2 alpha)/(g) ........(1)`
Case (ii) When angle of projection, `theta=45^(@)-alpha," let ",R=R_(2)` (say), then `R_(2)=(u^(2) sin 2(45^(@)-alpha))/(g)`
`=u^(2)/g sin (90^(@)-2alpha) =u^(2)/g cos 2 alpha .....(ii)`
From equation (i) and (ii), `R_(1)=R_(2)`
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