$A$ particle of mass $m$ is projected with velocity $v$ making an angle of $45^\circ$ with the horizontal. When the particle lands on the level ground,the magnitude of the change in its momentum will be

Two balls are thrown simultaneously from the ground with the same velocity of $10\,m/s$ but at different angles of projection with the horizontal. Both balls fall at the same distance $5\sqrt{3}\,m$ from the point of projection. What is the time interval between the balls striking the ground?

$A$ ring of mass $m$ moves from point $1$ to point $2$ along a smooth rigid horizontal wire with a constant speed $v$. The average force acting on the ring over the time of its motion from $1$ to $2$ is

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The angle of projection of the projectile is:

$A$ ball is projected from the ground at an angle of $45^{\circ}$ with the horizontal surface. It reaches a maximum height of $120 \ m$ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of $30^{\circ}$ with the horizontal surface. The maximum height it reaches after the bounce, in metres, is.

$A$ body of mass $1\,kg$ is projected with velocity $50\,m/s$ at an angle of $30^{\circ}$ with the horizontal. At the highest point of its path,a force of $10\,N$ starts acting on the body for $5\,s$ vertically upward in addition to the gravitational force. What is the horizontal range of the body? $\left(g=10\,m/s^2\right)$