$A$ projectile is launched with an initial speed of $40 \ m \ s^{-1}$ at an angle of $30^{\circ}$ above the ground. The projectile lands on a hillside $2.0 \ s$ later. The net displacement from where the projectile was launched to where it hits the target is (Take $g = 10 \ m \ s^{-2}$)

$A$ particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal,the maximum height attained by it equals $4R$. The angle of projection,$\theta$,is then given by

Two stones are projected so as to reach the same horizontal range on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the heights attained by them. Then,the angle of projection of the stone which attains the smaller height is $........$

The coordinates of a particle moving in a plane are given by $x = a \cos(pt)$ and $y = b \sin(pt)$,where $a, b (b < a)$ and $p$ are positive constants of appropriate dimensions. Then:

$A$ ball is hit by a batsman at an angle of $37^o$ with an initial velocity $u = 15 \ m/s$ as shown in the figure. The man standing at $P$ is at a distance of $9 \ m$ from the point $B$ where the ball would strike the ground. What is the minimum velocity at which the man should run to catch the ball before it hits the ground? Assume the height of the man is negligible. ........ $m/s$

Two projectiles $A$ and $B$ are thrown with the same speed such that $A$ makes an angle $\theta$ with the horizontal and $B$ makes an angle $\theta$ with the vertical. Then: