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JEE Mains · Physics · STD 11 - 3.2 motion in plane
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 \(45\)
Answer & Solution
Correct Answer
(B) \(60\)
Step-by-step Solution
Detailed explanation
\(\frac{u^{2}}{g}=100\) \(\Rightarrow u=20 \mathrm{m} / \mathrm{s}\) \(t=\frac{2 u \sin \theta}{g}\) and \(R=(u \cos \theta+20)\left(\frac{2 u \sin \theta}{g}\right)\) Put \(\frac{d R}{d \theta}=0\) \(\Rightarrow \cos \theta=1 / 2\) \(\Rightarrow \theta=60^{\circ}\)
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