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

A child stands on the edge of the cliff $10\,m$ above the ground and throws a stone horizontally with an initial speed of $5\,ms ^{-1}$. Neglecting the air resistance, the speed with which the stone hits the ground will be $..........ms ^{-1}$ (given, $g =10\,ms ^{-2}$)

An aeroplane flying at a constant velocity releases a bomb.As the bomb drops down from the aeroplane,

A ball is thrown from the location $\left(x_0, y_0\right)=(0,0)$ of a horizontal playground with an initial speed $v_0$ at an angle $\theta_0$ from the $+x$-direction. The ball is to be hit by a stone, which is thrown at the same time from the location $\left(x_1, y_1\right)=(L, 0)$. The stone is thrown at an angle $\left(180-\theta_1\right)$ from the $+x$-direction with a suitable initial speed. For a fixed $v_0$, when $\left(\theta_0, \theta_1\right)=\left(45^{\circ}, 45^{\circ}\right)$, the stone hits the ball after time $T_1$, and when $\left(\theta_0, \theta_1\right)=\left(60^{\circ}, 30^{\circ}\right)$, it hits the ball after time $T_2$. In such a case, $\left(T_1 / T_2\right)^2$ is. . . . .

Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buldings $100 \;\mathrm{m}$ apart and of same helght of $200 \;\mathrm{m}$ with the same velocity of $25\; \mathrm{m} / \mathrm{s}$. When and where will the two bullets collide. $\left(g=10 \;\mathrm{m} / \mathrm{s}^{2}\right)$

A ball is rolled off the edge of a horizontal table at a speed of $4\, m/second$. It hits the ground after $0.4\, second$. Which statement given below is true