Motion in a Plane

Two bodies are projected with the same velocity. If one is projected at an angle of $30^\circ$ and the other at $45^\circ$ to the horizontal, then the ratio of maximum heights attained is

In the projectile motion of a particle on a level ground, which of the following remains constant with reference to time and position?

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

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

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

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 i...

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