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 $|\overrightarrow{A}| = ..........$

(N/A) The horizontal range $R$ of a projectile is given by $R = \frac{v^2 \sin(2\theta)}{g}$. For $R$ to be maximum,$\sin(2\theta) = 1$,which implies $2\theta = 90^{\circ}$,so $\theta = 45^{\circ}$.
$(b)$ For uniform circular motion,the acceleration is centripetal (directed towards the center) and the velocity is tangential. The angle between the tangent and the radius at the point of contact is $90^{\circ}$.
$(c)$ The magnitude of vector $\overrightarrow{A} = 4\widehat{i} + 3\widehat{j}$ is $|\overrightarrow{A}| = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$.