A ball is projected from the ground at an angle of $45^{\circ}$ with the horizontal surface. It reaches a maximum height of $120 m$ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of $30^{\circ}$ with the horizontal surface. The maximum height it reaches after the bounce, in metres, is. . . . .
$20$
$30$
$40$
$50$
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
An aeroplane moving horizontally with a speed of $720 \,km/h$ drops a food pocket, while flying at a height of $396.9\, m$. the time taken by a food pocket to reach the ground and its horizontal range is (Take $g = 9.8 m/sec^{2}$)
A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement time graph is characterised by
A ball rolls from the top of a stair way with a horizontal velocity $u\; m /s$ . If the steps are $h\; m$ high and $b\; m$ wide, the ball will hit the edge of the $n^{th}$ step, if $n=$
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?
($AV$) $\vec{u}_0=\sqrt{2 g h} \hat{x}$ ($B$) $\vec{v}=\sqrt{2 g h}(\hat{x}-\hat{z})$ ($C$) $\theta=60^{\circ}$ ($D$) $d / h_1=2 \sqrt{3}$