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  4. The maximum range of a projectile fired with some initial velocity is found to be 1000 metre, in the absence of wind and air resistance. The maximum height h reached by this projectile is

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Q. The maximum range of a projectile fired with some initial velocity is found to be 1000 metre, in the absence of wind and air resistance. The maximum height h reached by this projectile is

JIPMERJIPMER 2013Motion in a Plane

Solution:

$R_{max} = \frac{u^2}{g} = 1000 m $
(R is maximum when $\theta$ = 45°)
$H = \frac{u^2 \, \sin^2 \, \theta}{2g} = \frac{u^2}{2g} \times \sin^2 \, 45^\circ$
$ = \frac{1000}{4} = 250 \, m$