$A$ wheel of radius $R$ is trapped in a mud pit and spinning. As the wheel is spinning,it splashes mud blobs with initial speed $u$ from various points on its circumference. The maximum height from the centre of the wheel,to which a mud blob can reach is

$A$ cyclist starts from the centre $O$ of a circular park of radius $1 \text{ km}$,reaches the edge $P$ of the park. Then,the cyclist cycles along the circumference to point $Q$ and returns to the centre along $QO$ as shown in the figure. If the round trip takes $10 \text{ minutes}$,the net displacement and average speed of the cyclist (in metre and kilometre per hour respectively) are:

$A$ particle moving in $x-y$ plane starts from the origin at $t=0$ with an initial velocity $(-\hat{i}+\hat{j}) \,ms^{-1}$ and undergoes an acceleration of $(6 \hat{i}+4 \hat{j}) \,ms^{-2}$. Its displacement after $2 \,s$ is (in $\,m$)

$A$ projectile is launched from point $A$ of the given landscape with a water body as shown in the diagram. The launching angle is $15^{\circ}$. From the following, identify the right initial velocity of the projectile with which it will fall somewhere in between the points $C$ and $D$. [Assume $g = 10 \,m/s^2$] (in $\,m/s$)

Two objects of equal mass are projected with the same velocity $v$ at the same angle $\theta$ towards each other from a distance $R$. What is the momentum of the system at the moment of collision?

$A$ point moves in the $xy$-plane according to the following equations: $x = a \sin \omega t$ and $y = a(1 - \cos \omega t)$, where $a$ and $\omega$ are positive constants. Find the angle between the point's velocity and acceleration vectors.