$A$ particle is projected upwards with a velocity of $100 \ m/s$ at an angle of $60^{\circ}$ with the vertical. Find the time when the particle will move perpendicular to its initial direction,$.....$ seconds (take $g = 10 \ m/s^2$):-

If a ball can be thrown to a maximum horizontal distance of $80 \, m$,what is the maximum height to which it can be thrown (in $, m$)?

$A$ missile is fired for maximum range with an initial velocity of $20\; m/s$. If $g = 10\; m/s^2$,the range of the missile is ...... $m$.

If a body is projected with an angle $\theta$ to the horizontal, then

Two bodies are projected at angles $\theta$ and $(90^\circ - \theta)$ with the same initial velocity. Find the ratio of their times of flight.

$A$ ball is projected at an angle $45^{\circ}$ with the horizontal. It passes through a wall of height $h$ at a horizontal distance $d_1$ from the point of projection and strikes the ground at a horizontal distance $(d_1 + d_2)$ from the point of projection. Then $h$ is: