Starting from the origin at time $t=0$ , with initial velocity $5\hat{j}{\mathrm{m}\mathrm{s}}^{-1}$ , a particle moves in the $x$$-y$ plane with a constant acceleration of $(10\hat{i}+4\hat{j}){\mathrm{m}\mathrm{s}}^{-2}$ . At time $t$ , its coordinates are $(20$ $\left.m,y_{0}m\right)$ . The values of $t$ and $y_0$ are, respectively:

Time period of a simple pendulum in a stationary lift is ‘T’. If the lift accelerated with $\frac{g}{6}$ vertically upwards then the time period will be:

(Where g = acceleration due to gravity)

Two vectors $\overrightarrow{A}and\overrightarrow{B}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> have equal magnitudes. If magnitude of <!-- [if gte mso 9]><xml> </xml><![endif]-->  $\overrightarrow{A}+\overrightarrow{B}$ is equal to two times the magnitude of <!-- [if gte mso 9]><xml> </xml><![endif]-->  $\overrightarrow{A}-\overrightarrow{B},$ then the angle between $\overrightarrow{A}and\overrightarrow{B}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> will be:

If $\overline{A}=\left(2\widehat{i}+3\widehat{j}-\widehat{k}\right)mand\overrightarrow{B}=\left(\widehat{i}+2\widehat{j}+2\widehat{k}\right)m.$ The magnitude of component of vector $\overrightarrow{A}$ along vector $\overrightarrow{B}$ will be________m.

If the initial velocity in horizontal direction of a projectile is unit vector $\widehat{i}$ and the equation of trajectory is y = 5x(1 – x). The y component vector of the initial velocity is ________ $\widehat{j}$ .

Two projectiles thrown at $30°and45°$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is: