Question

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y= (4t - 2t 2 )m and x=(3t)metre, where t is in seconds and point of projection is taken as origin. The angle of projection of projectile with vertical is:- a) 30 degree b) 37 degree c) 45 degree d) 60 degree

Answer 1

Ф = angle of projection with horizontal.

y = (4 t - 2 t²) meters  = u sinФ t - g x² sec² Ф /(2 u²)
x = u cos Ф t = 3 t   meters

so   u cosФ = 3    ,       u sinФ  = 4,            g sec²Ф /2u² = 2
        tanФ = 4/3           sinФ = 4/5
=>  u = 5  m/s       g = 36 m/s²

angle of projection with vertical = 37 deg.  

Answer 2

Answer:

53°

Explanation:

let $\alpha$ = angle of projection with horizontal.

⇒ y = (4 t - 2 t²) meters  

comparing with  $y = u . sin \alpha . t - \frac{1}{2} g t^{2}$

∴ u sin α = 4

and

$\frac{1}{2} g = 2$

⇒ x = u cos α.  t = 3 t   meters

so   u cos α = 3    -- [1]

     u sin α   = 4,     --[2]  

   g /2 = 2             --[3]

     

=> [2] / [1]

tan α = 4/3

∵ tan 4/3 = 53 °

∴ α = 53°

angle of projection with vertical =α = 53°