An aeroplane moving horizontally with a speed of $180\, km/hr$. drops a food packet while flying at a height of $490\,m$. The horizontal range is........$m$
$180$
$980$
$500$
$670$
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, $g =10\,ms ^{-2}$)
A body is projected horizontally with a velocity of $4\,m / s$ from the top of a high tower. The velocity of the body after $0.7\,s$ is nearly $.....\,m/s$ (take $g=10\,m / s ^2$ )
A slide with a frictionless curved surface, which becomes horizontal at its lower end,, is fixed on the terrace of a building of height $3 h$ from the ground, as shown in the figure. A spherical ball of mass $\mathrm{m}$ is released on the slide from rest at a height $h$ from the top of the terrace. The ball leaves the slide with a velocity $\vec{u}_0=u_0 \hat{x}$ and falls on the ground at a distance $d$ from the building making an angle $\theta$ with the horizontal. It bounces off with a velocity $\overrightarrow{\mathrm{v}}$ and reaches a maximum height $h_l$. The acceleration due to gravity is $g$ and the coefficient of restitution of the ground is $1 / \sqrt{3}$. Which of the following statement($s$) is(are) correct?
($AV$) $\vec{u}_0=\sqrt{2 g h} \hat{x}$ ($B$) $\vec{v}=\sqrt{2 g h}(\hat{x}-\hat{z})$ ($C$) $\theta=60^{\circ}$ ($D$) $d / h_1=2 \sqrt{3}$
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. . . . .