The angle of projection for a projectile to have same horizontal range and maximum height is :

The co-ordinates of a particle moving in $$x$$-$$y$$ plane are given by : $$x=2+4 \mathrm{t}, y=3 \mathrm{t}+8 \mathrm{t}^2$$.

The motion of the particle is :

Projectiles A and B are thrown at angles of $$45^{\circ}$$ and $$60^{\circ}$$ with vertical respectively from top of a $$400 \mathrm{~m}$$ high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $$v_A: v_B$$ is :

[Take $$g=10 \mathrm{~ms}^{-2}$$]

Position of an ant ($$\mathrm{S}$$ in metres) moving in $$\mathrm{Y}$$-$$\mathrm{Z}$$ plane is given by $$S=2 t^2 \hat{j}+5 \hat{k}$$ (where $$t$$ is in second). The magnitude and direction of velocity of the ant at $$\mathrm{t}=1 \mathrm{~s}$$ will be :