A particle is projected with speed $u$ at angle $\theta$ with horizontal from ground. If it is at same height from ground at time $t_1$ and $t_2$, then its average velocity in time interval $t_1$ to $t_2$ is

Q. From the top of a building, a particle is projected up at an angle $\theta$ with horizontal and reaches the ground in time $t_1$. A second particle projected down at an angle $\theta$ with horizontal and with same speed reaches the ground in time $t_2$. If third particle projected horizontally with same speed reaches the ground in time $t_3$, then

Q. A body is thrown upward at an angle $\theta$ with horizontal from a point A on top of a tower. It reaches ground in time $t_1$. If it is thrown downward at an angle $\theta$ with horizontal from same point with same speed, it reaches the ground in time
$t_2$. If it is allowed to fall freely from A, then the time it takes to reach the ground is given by

Q. A particle is projected from the ground at $t=0$ so that on its way it just clears two vertical walls of equal height on the ground. The particle was projected with initial velocity $u$ and at angle $\theta$ with the horizontal. If the particle passes just grazing top of the wall at time $t=t_1$ and $t=t_2$ then calculate.
a. the height of the wall.
b. the time $t_1$ and $t_2$ in terms of height of the wall. Write the expression for calculating the range of this projecting and separation between the walls.

Q. A particle is projected from the ground at an angle of $\theta$ with the horizontal with an initial speed of $u$. Find the final velocity when it is perpendicular to the initial velocity.

Q. A body is projected up with velocity $u$. It reaches the same point in its path at $t_1$ and $t_2$ from the time of projection. Then $t_1+t_2$ is: