Maximum range of a bullet fired from a toy pistol mounted on a car at rest is R

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3-2.Motion in Plane

hard

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is $R_0= 10\, m$. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $v = 20\, m/s$, on a horizontal surface ......... $^o.$ $(g = 10\, m/s^2)$

A$30$

B$60$

C$75$

D$45$

(JEE MAIN-2013)

Solution

$\frac{u^{2}}{g}=100$
$\Rightarrow u=20 \mathrm{m} / \mathrm{s}$
$t=\frac{2 u \sin \theta}{g}$
and $R=(u \cos \theta+20)\left(\frac{2 u \sin \theta}{g}\right)$
Put $\frac{d R}{d \theta}=0$
$\Rightarrow \cos \theta=1 / 2$
$\Rightarrow \theta=60^{\circ}$

Standard 11

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hard

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