A particle is projected at an angle of $30^{\circ}$ from horizontal at a speed of $60 \mathrm{~m} / \mathrm{s}$. The height traversed by the particle in the first second is $\mathrm{h}_0$ and height traversed in the last second, before it reaches the maximum height, is $h_1$. The ratio $h_0: h_1$ is __________.

[Take, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ]

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of $$100 \mathrm{~m}$$ from the foot of the tower. A body of mass $$2 \mathrm{~M}$$ thrown at a velocity $$\frac{v}{2}$$ from the top of the tower of height $$4 \mathrm{H}$$ will touch the ground at a distance of _______ m.

The maximum height reached by a projectile is $$64 \mathrm{~m}$$. If the initial velocity is halved, the new maximum height of the projectile is ______ $$\mathrm{m}$$.

A ball rolls off the top of a stairway with horizontal velocity $$u$$. The steps are $$0.1 \mathrm{~m}$$ high and $$0.1 \mathrm{~m}$$ wide. The minimum velocity $$u$$ with which that ball just hits the step 5 of the stairway will be $$\sqrt{x} \mathrm{~ms}^{-1}$$ where $$x=$$ __________ [use $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$ ].