$A$ car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud,as they leave the ground,are thrown:

$A$ body of mass $m$ is projected at an angle of $45^{\circ}$ with the horizontal with an initial velocity $v$. If air resistance is negligible,then the total change in momentum when it strikes the ground is:

An aircraft is flying at a height of $H$ above the ground at a constant speed $V$. What is the maximum angle subtended at a ground observation point by the aircraft's path after time $T$?

$A$ particle is rotating in a circle of radius $1\,m$ with constant speed $4\,m/s$. In time $1\,s$,match the following (in $SI$ units) columns.

Column $I$	Column $II$
$(A)$ Displacement	$(p)$ $8 \sin 2$
$(B)$ Distance	$(q)$ $4$
$(C)$ Average velocity	$(r)$ $2 \sin 2$
$(D)$ Average acceleration	$(s)$ $4 \sin 2$

What is the value of linear velocity,if $\vec \omega = 3\hat i - 4\hat j + \hat k$ and $\vec r = 5\hat i - 6\hat j + 6\hat k$?

$A$ 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