A projectile is given an initial velocity of $\hat{\mathrm{i}}+2\hat{\mathrm{j}} \mathrm{m} {\mathrm{s}}^{-1},$ where $\hat{i}$ is along the ground and $\hat{\mathrm{j}}$ is along the vertical. If $g=10 \mathrm{m} {\mathrm{s}}^{-2},$ the equation of its trajectory is

A plane is inclined at an angle $\mathrm{\alpha }=30°$ with respect to the horizontal. A particle is projected with a speed $u=2 \mathrm{m} {\mathrm{s}}^{-1}$ from the base of the plane making an angle $\mathrm{\theta }=15°$ with respect to the plane as shown in the figure. The distance from the base at which the particle hits the plane is close to:
(Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

A particle is initially at rest. It is subjected to linear acceleration $a$, as shown in the figure. The maximum speed attained by the particle is,