The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

A particle has initial velocity $$\left( {2\overrightarrow i + 3\overrightarrow j } \right)$$ and acceleration $$\left( {0.3\overrightarrow i + 0.2\overrightarrow j } \right)$$. The magnitude of velocity after 10 seconds will be

The potential energy of a particle in a force field is $$U = {A \over {{r^2}}} - {B \over r}$$ where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is

Two spheres A and B of masses m₁ and m₂ respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity $${v \over 2}$$ in a direction perpendicular to the original direction. The mass A moves after collision in the direction :