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  4. A rifle with a muzzle velocity of 100 m s- 1 shoots a bullet at a small target 30 m away in the same horizontal line. How high above the target must the gun be aimed so that the bullet will hit the target?

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Q. A rifle with a muzzle velocity of $100 \, m \, s^{- 1}$ shoots a bullet at a small target $30 \, m$ away in the same horizontal line. How high above the target must the gun be aimed so that the bullet will hit the target?

NTA AbhyasNTA Abhyas 2020Motion in a Straight Line

Solution:

$3 0 = \frac{\text{u}^{2} \text{sin2} \theta }{\text{g}} \Rightarrow 3 0 \times 1 0 = 1 0 0^{2} \text{sin} 2 \theta $
$\text{sin2} \theta = 0 \text{.} 0 3 \Rightarrow 2 \theta = 0 \text{.} 0 3$
$\theta = 0 \text{.} 0 1 5 \Rightarrow \text{tan} \theta = 0 \text{.} 0 1 5$
$\frac{\text{h}}{3 0} = 0 \text{.} 0 1 5 \Rightarrow \text{h} = 0 \text{.} 4 5 \, \text{m}$
Solution