$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The height of each wall is ........ $m$.

$A$ particle has an initial velocity of $(3\hat i + 4\hat j) \; ms^{-1}$ and an acceleration of $(0.4\hat i + 0.3\hat j) \; ms^{-2}$. Its speed after $10 \; s$ is:

Three particles,located initially on the vertices of an equilateral triangle of side $L$,start moving with a constant speed $v$ towards each other in a cyclic manner,forming spiral loci that converge at the centroid of the triangle. The length of one such spiral locus will be

Fill in the blanks given below:
$(a)$ At an angle of .......... the horizontal range of a projectile is maximum.
$(b)$ The angle between the instantaneous velocity and instantaneous acceleration of a particle moving in a circular path with constant speed is ..........
$(c)$ If $\overrightarrow{A} = 4\widehat{i} + 3\widehat{j}$,then $|\overrightarrow{A}| = ..........$

$A$ particle of mass $m$ is projected at a velocity $u$,making an angle $\theta$ with the horizontal ($x$-axis). If the angle of projection $\theta$ is varied keeping all other parameters same,then the magnitude of angular momentum $(L)$ at its maximum height about the point of projection varies with $\theta$ as,

$A$ body of mass $0.5 \,kg$ is projected under gravity with a speed of $98 \,m/s$ at an angle of $30^\circ$ with the horizontal. The change in momentum (in magnitude) of the body is ......... $N-s$.