Kinematics Questions

When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ }$ with horizontal, it can travel a distance $x_1$ along the plane. But when the inclination is decreased to $30^{\circ }$ and the same object is shot with the same velocity, it can travel $x_2$ distance. Then $x_1:x_2$ will be:

Two bullets are fired horizontally and simultaneously towards each other from the rooftops of two buildings (building distance being $200\text{m}$ apart and being of the same height of $200\text{m}$) with the same velocity of $25\text{m/s}$. When and where will the two bullets collide? ($g=10{\text{m/s}}^2$)

A particle starting from rest moves in a circle of radius $r$. It attains a velocity of $v_0\text{m/s}$ on completion of $n$ rounds. Its angular acceleration will be:

A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time $t_1$ if the elevator is moving uniformly and time $t_2$ if the elevator is stationary. Then:

A person travelling in a straight line moves with a constant velocity $v_1$ for a certain distance $x$ and with a constant velocity $v_2$ for the next equal distance. The average velocity $v$ is given by the relation:

A mass falls from a height $h$ and its time of fall is recorded as $t$ in terms of time period $T$ of a simple pendulum. On the surface of the earth, it is found that $t=2T$. The entire setup is taken on the surface of another planet whose mass is half of that of the Earth and whose radius is the same. The same experiment is repeated and corresponding times are noted as $t^{\prime }$ and $T^{\prime }$. Then we can say: