Question # A projectile is given an initial velocity of ( (i+2 i) mathrm{m} / mathrm{s} ), where ( i ) is along the ground and ( hat{j} ) is along the vertical.

# A projectile is given an initial velocity of ( (i+2 i) mathrm{m} / mathrm{s} ), where ( i ) is along the ground and ( hat{j} ) is along the vertical.

If ( g=10 mathrm{m} / mathrm{s}^{2} ), the equation of its trajectory is:

[llT Main 2013]

(A) ( 4 y=2 x-25 x^{2} )

(B) ( y=x-5 x^{2} )

(C) ( y=2 x-5 x^{2} )

(D) ( 4 y=2 x-5 x^{2} )

Solution

( U_{x}=I quad U_{Y}=2 quad tan theta 2 )

( y=n tan theta=frac{g x^{2}}{2 u^{2} cos ^{2} theta} quad u^{2}=5 )

( y=2 x-frac{10 x^{2} sec ^{2} theta}{10} )

( =2 x-x^{2}left(1+tan ^{2} alpharight) )

( y=2 x-5 x^{2}(c) ) Ans siverative