A plane is inclined at an angle $\alpha =30°$ 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 $\theta =15°$ 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, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

In a three-dimensional system, the position coordinates of a particle (in motion) are given below $x=a\cos \omega t, y=a\sin \omega t, z=a\omega t$. The velocity of the particle will be

A rough inclined plane $BCE$ of height $\left(\frac{25}{6}\right) \mathrm{m}$ is kept on a rectangular wooden block $ABCD$ of height $10 \mathrm{m}$, as shown in the figure. A small block is allowed to slide down from the top $E$ of the inclined plane. The coefficient of kinetic friction between the block and the inclined plane is $\frac{1}{8}$ and the angle of inclination of the inclined plane is ${\sin }^{-1}\left(0.6\right)$. If the small block finally reaches the ground at a point $F$, then $DF$ will be (Acceleration due to gravity, $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)

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