For a train engine moving with speed of $20 {\mathrm{ms}}^{–1}$, the driver must apply brakes at a distance of $500 \mathrm{m}$ before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed $\sqrt{x} {\mathrm{ms}}^{-1}$. The value of $x$ is ______. (Assuming same retardation is produced by brakes)

The magnitude of vectors $\overrightarrow{\mathrm{OA}}, \overrightarrow{\mathrm{OB}}$ and $\overrightarrow{\mathrm{OC}}$ in the given figure are equal. The direction of $\overrightarrow{\mathrm{OA}}+\overrightarrow{\mathrm{OB}}-\overrightarrow{\mathrm{OC}}$ with $x-$axis will be:

Two spherical balls having equal masses with radius of $5 \mathrm{cm}$ each are thrown upwards along the same vertical direction at an interval of $3 \mathrm{s}$ with the same initial velocity of $35 \mathrm{m} {\mathrm{s}}^{-1}$, then these balls collide at a height of _____$\mathrm{m}$,

(take $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The angle between vector $\left(\overrightarrow{A}\right)$ and $(\overrightarrow{A}-\overrightarrow{B})$ is :

The resultant of these forces $\overrightarrow{OP},\overrightarrow{OQ},\overrightarrow{OR},\overrightarrow{OS}$ and $\overrightarrow{OT}$ is approximately ______$\mathrm{N}.$
[Take $\sqrt{3}=1.7,\sqrt{2}=1.4$ Given $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ unit vectors along $x, y$ axis]