If the magnitude of a vector $\mathbf{P}$ is 25 units and its $y$-component is 7 units, then its $x$-component is

The height of ceiling in an auditorium is 30 m . A ball is thrown with a speed of $30 \mathrm{~ms}^{-1}$ from the entrance such that it just moves very near to the ceiling without touching it and then it reaches the ground at the end of the auditorium. Then, the length of auditorium is [Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ ]

A balloon with mass ' $m$ ' is descending vertically with an acceleration ' $a$ ' (where $a

A conveyor belt is moving horizontally with a velocity of $2 \mathrm{~ms}^{-1}$. If a body of mass 10 kg is kept on it, then the distance travelled by the body before coming to rest is

(The coefficient of kinetic friction between the belt and the body is 0.2 and acceleration due to gravity is $10 \mathrm{~ms}^{-2}$ )