Two objects are projected at an angle $$\theta^{\circ}$$ and $$\left(90-\theta^{\circ}\right)$$, to the horizontal with the same speed. The ratio of their maximum vertical heights is

The maximum range of a gun on horizontal plane is $$16 \mathrm{~km}$$. If $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$, then muzzle velocity of a shell is

The trajectory of projectile is

For a projectile motion, the angle between the velocity and acceleration is minimum and acute at

A particle starts from the origin at $$t=0$$ with a velocity of $$10 \hat{\mathbf{j}} \mathrm{ms}^{-1}$$ and move in the $$x$$-$$y$$ plane with a constant acceleration of $$(8 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}) \mathrm{ms}^{-2}$$. At an instant when the $$x$$-coordinate of the particle is $$16 \mathrm{~m}, y$$-coordinate of the particle is

Rain is falling vertically with a speed of $$12 \mathrm{~ms}^{-1}$$. A woman rides a bicycles with a speed of $$12 \mathrm{~ms}^{-1}$$ in east to west direction. What is the direction in which she should hold her umbrella?

The trajectory of a projectile projected from origin is given by the equation $$y=x-\frac{2 x^2}{5}$$. The initial velocity of the projectile is