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?

Question

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? (A) 0.45m (B) 0.60m (C) 0.75m (D) 0.90m

Tardigrade Admin · Accepted Answer

3 0 = ( textu2 textsin2 θ / textg) ⇒ 3 0 × 1 0 = 1 0 02 textsin 2 θ textsin2 θ = 0 text. 0 3 ⇒ 2 θ = 0 text. 0 3 θ = 0 text. 0 1 5 ⇒ texttan θ = 0 text. 0 1 5 ( texth/3 0) = 0 text. 0 1 5 ⇒ texth = 0 text. 4 5 textm <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-mh6qdhdqbxs6.png" />

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?

$0.45 m$

$0.60 m$

$0.75 m$

$0.90 m$

$30 = \frac{u ^{2} sin2 θ}{g} \Rightarrow 30 \times 10 = 10 0^{2} sin 2 θ$
$sin2 θ = 0.03 \Rightarrow 2 θ = 0.03$
$θ = 0.015 \Rightarrow tan θ = 0.015$
$\frac{h}{30} = 0.015 \Rightarrow h = 0.45 m$

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

0.45m

0.60m

0.75m

0.90m