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 particle crossing the origin at time $t=0$ moves in the $X Y$-plane with a constant acceleration ' $a$ ' in $y$-direction. If the equation of motion of the particle is $y=b x^2$ (where $b$ is a constant), then its velocity component in the $x$-direction is

If a ball projected vertically upwards with certain initial velocity from the ground crosses a point at a height of 25 m twice in a time interval of 4 s , then the initial velocity of the ball is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A car is moving with a velocity of $4 \mathrm{~ms}^{-1}$ towards east. After a time of 4 s , if it is heading north-east with a velocity of $4 \sqrt{2} \mathrm{~ms}^{-1}$, then the average velocity of the car is