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 mouse jumps off from the $15$ th floor of a high-rise building and lands $12 \,m$ from the building. Assume that, each floor is of $3 \,m$ height. The horizontal speed with which the mouse jumps is closest to ...............$km /h$
A body is thrown horizontally from the top of a tower of height $5 \,m$. It touches the ground at a distance of $10 \,m$ from the foot of the tower. The initial velocity of the body is ......... $ms^{-1}$ ($g = 10\, ms^{-2}$)
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 particles are simultaneously projected in opposite directions horizontally from a given point in space, where gravity $g$ is uniform. If $u_1$ and $u_2$ be their initial speeds, then the time $t$ after which their velocities are mutually perpendicular is given by
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 $g = 9.8 m/sec^{2}$)