A particle is projected from a point O with velocity $u$ at an angle of $60^\circ$ with the horizontal. When it is moving in a direction at right angles to its direction at $O$, its velocity then is given by
(1) $\frac{u}{3}$
(2) $\frac{u}{2}$
(3) $\frac{2u}{3}$
(4) $\frac{u}{\sqrt{3}}$

A body is projected at $t = 0$ with a velocity $10 \mathrm {~ms} ^ { - 1 }$ at an angle of $60 ^ { \circ }$ with the horizontal. The radius of curvature of its trajectory at $t = 1 \mathrm {~s}$ is $R$. Neglecting air resistance and taking acceleration due to gravity $\mathrm { g } = 10 \mathrm {~ms} ^ { - 2 }$, the value of $R$ is:
(1) 10.3 m
(2) 2.8 m
(3) 2.5 m
(4) 5.1 m

A projectile is projected at $30 ^ { \circ }$ from horizontal with initial velocity $40 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The velocity of the projectile at $\mathrm { t } = 2 \mathrm {~s}$ from the start will be:
(1) $40 \sqrt { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) Zero
(3) $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $20 \sqrt { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$