The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y=(4 t-2 t2) m and x=(3 t) metre, where t is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is

Question

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y=(4 t-2 t2) m and x=(3 t) metre, where t is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is (A) 30° (B) 37° (C) 45° (D) 60°

Tardigrade Admin · Accepted Answer

y=4 t-2 t2 x=3 t V=Vx hati+Vy hatj Vx=(d x/d t), Vy=(d y/d t) Vx=3, Vy=4-4 t for t=0, Vy=4 tan θ=(Vy/Vx)=(4/3) θ=53° with horizontal With vertical θ=37°

Q. The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by $y = (4 t - 2 t^{2}) m$ and $x = (3 t)$ metre, where $t$ is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is

$3 0^{\circ}$

$3 7^{\circ}$

$4 5^{\circ}$

$6 0^{\circ}$

$y = 4 t - 2 t^{2}$
$x = 3 t$
$V = V_{x \hat{i}} + V_{y \hat{j}}$
$V_{x} = \frac{d x}{d t}, V_{y} = \frac{d y}{d t}$
$V_{x} = 3, V_{y} = 4 - 4 t$
for $t = 0, V_{y} = 4$
$tan θ = \frac{V _{y}}{V _{x}} = \frac{4}{3}$
$θ = 5 3^{\circ}$ with horizontal With vertical
$θ = 3 7^{\circ}$

Q. The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y=(4t−2t2)m and x=(3t) metre, where t is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is

30∘

37∘

45∘

60∘