A particle is projected with a velocity of $30\,m / s$, at an angle of $\theta_0=\tan ^{-1}\left(\frac{3}{4}\right)$ After $1\,s$, the particle is moving at an angle $\theta$ to the horizontal, where $\tan \theta$ will be equal to $\left(g=10\,m / s ^2\right)$

Two projectiles, one fired from surface of earth with velocity $10 \,m/s$ and other fired  from the surface of another planet with initial speed $5\, m/s$ trace identical trajectories.  The value of acceleration due to the gravity on the planet is   ......... $m/s^2$

The $x-t$ graph of a particle moving along a straight line is shown in figure The speed-time graph of the particle is correctly shown by

 The $x-t$ graph of a particle moving along a straight line is shown in figure The $v-t$ graph of the particle is correctly shown by

Aball is thrown from a point on ground at some angle of projection. At the same time a bird starts from a point directly above this point of projection at a height $h$ horizontally with speed $u$. Given that in its flight ball just touches the bird at one point. Find the distance on ground where ball strikes

On which does the value of range depend ? On which does the maximum value of range depend ?