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-5x^(2)`
C. `4y=2x-5x^(2)`
D. `y=2x-25x^(2)`

Answer

A

Explanation

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