Kinematics · JEE Advanced previous year questions

A projectile of mass $200\mathrm{g}$ is launched in a viscous medium at an angle $60^{\circ }$ with the horizontal, with an initial velocity of $270m/s$. It experiences a viscous drag force $\vec{F}=-c\vec{v}$ where the drag coefficient $c=0.1kg/s$ and $\vec{v}$ is the instantaneous velocity of the projectile. The projectile hits a vertical wall after $2\mathrm{s}$. Taking $e=2.7$, the horizontal distance of the wall from the point of projection (in $\mathrm{m}$) is ____

1. A.${\vec{u}}_0=\sqrt{2gh}\hat{x}$
2. B.$\vec{v}=\sqrt{2gh}(\hat{x}-\hat{z})$
3. C.$\theta =60^{\circ }$
4. D.$d/h_1=2\sqrt{3}$

A person of height $1.6\mathrm{m}$ is walking away from a lamp post of height $4\mathrm{m}$ along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is $60\mathrm{cm}{\mathrm{s}}^{-1}$, the speed of the tip of the person's shadow on the ground with respect to the person is ____ $\mathrm{cm}{\mathrm{s}}^{-1}$.