An artillery piece which consistently shoots its shells with the same muzzle speed has a maximum range R . To hit a target which is (R/2) from the gun and on the same level, the angle of elevation of the gun should be

Question

An artillery piece which consistently shoots its shells with the same muzzle speed has a maximum range R . To hit a target which is (R/2) from the gun and on the same level, the angle of elevation of the gun should be (A) 15°  (B) 45°  (C) 30°  (D) 60°

Tardigrade Admin · Accepted Answer

R textmax=R=(u2/g) (at an angle of 45° ) u2=Rg Using textRange=(u2 textsin 2 θ /g) then (R/2)=( textitRg)( textsin 2 θ /g) textsin 2 θ = (1/2) 2θ =30° ⇒ θ =15°

Q. An artillery piece which consistently shoots its shells with the same muzzle speed has a maximum range $R$ . To hit a target which is $\frac{R}{2}$ from the gun and on the same level, the angle of elevation of the gun should be

$1 5^{\circ}$

$4 5^{\circ}$

$3 0^{\circ}$

$6 0^{\circ}$

$R_{max} = R = \frac{u ^{2}}{g}$ (at an angle of $4 5^{\circ}$ )
$u^{2} = R g$
Using $Range = \frac{u ^{2} sin 2 θ}{g}$
then $\frac{R}{2} = (Rg) \frac{sin 2 θ}{g}$
$sin 2 θ = \frac{1}{2}$
$2 θ = 3 0^{\circ} \Rightarrow θ = 1 5^{\circ}$

Q. An artillery piece which consistently shoots its shells with the same muzzle speed has a maximum range R . To hit a target which is 2R​ from the gun and on the same level, the angle of elevation of the gun should be

15∘

45∘

30∘

60∘