A projectile is given an initial velocity of ` ( hat(i) + 2 hat (j) ) m//s`, where ` hat(i)` is along the ground and `hat (j)` is along the vertical . If ` g = 10 m//s^(2) `, the equation of its trajectory is :

Options

A. `y = 2x - 5x^2`
B. `y =x - 5 x^2`
C. `4 y = 2x - 5x^2`
D. `y = 2x - 25 x^2`

Answer

A

Explanation

(a) `tan theta = (u sin theta)/(u cos theta) = (2)/(1)`
The desired equation is
`y = x tan theta - (g x^2)/(2 u^2 cos^2 theta) = x xx 2 - (10 x^2)/(2 (sqrt(2^2 + 1^2))^(2)((1)/(sqrt(5)))^2`
or `y = 2x - 5 x^2`.