For a projectile thrown into air with a speed (v) the horizontal range is (√3 v 2/2 g ) and the vertical height is ( v 2/8 g ). The angle which the projectile makes with the horizontal initially is

Question

For a projectile thrown into air with a speed (v) the horizontal range is (√3 v 2/2 g ) and the vertical height is ( v 2/8 g ). The angle which the projectile makes with the horizontal initially is (A) 15° (B) 30° (C) 45° (D) 60°

Tardigrade Admin · Accepted Answer

R =(√3 v 2/2 g )=( v 2 sin 2 θ/ g ) sin 2 θ=(√3/2) 2 θ=60° θ=30°

Q. For a projectile thrown into air with a speed (v) the horizontal range is $\frac{3 v ^{2}}{2 g}$ and the vertical height is $\frac{v ^{2}}{8 g}$ . The angle which the projectile makes with the horizontal initially is

$1 5^{\circ}$

$3 0^{\circ}$

$4 5^{\circ}$

$6 0^{\circ}$

$R = \frac{3 v ^{2}}{2 g} = \frac{v ^{2} s i n 2 θ}{g}$
$sin 2 θ = \frac{3}{2}$
$2 θ = 6 0^{\circ}$
$θ = 3 0^{\circ}$

Q. For a projectile thrown into air with a speed (v) the horizontal range is 2g3​v2​ and the vertical height is 8gv2​. The angle which the projectile makes with the horizontal initially is

15∘

30∘

45∘

60∘