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  • The maximum range of a bullet fired from a toy pistol mounted on a car at rest is  What will

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is R_{0}=40m. 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 \upsilon =20m/s, on a horizontal surface? 

\left ( g=10m/s^{2} \right )

Option: 1

30^{\circ}


Option: 2

60^{\circ}


Option: 3

75^{\circ}


Option: 4

45^{\circ}


Answers (1)

best_answer

 

 

 

Initially

\begin{aligned} &\frac{u^{2}}{g}=40\\ &\Rightarrow u=20 \mathrm{m} / \mathrm{s} \end{aligned}

When a car is moving

then u_x=20+ucos\theta \\ and \ u_y=usin\theta

So 

\begin{aligned} &t=\frac{2 u \sin \theta}{g}\\ &\text { and } R=(u \cos \theta+20)\left(\frac{2 u \sin \theta}{g}\right)\\ &\text { Put } \frac{d R}{d \theta}=0\\ &\Rightarrow \cos \theta=1 / 2\\ &\Rightarrow \theta=60^{\circ} \end{aligned}

Posted by

Ritika Jonwal

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