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. . . . .
$2$
$0$
$3$
$4$
An aeroplane is moving with a velocity $u$. It drops a packet from a height $h$. The time $t$ taken by the packet in reaching the ground will be
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 bomb is dropped from an aeroplane moving horizontally at constant speed. When air resistance is taken into consideration, the bomb
At the height $80 \,m$, an aeroplane is moving with $150\, m/s$. A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped ......... $m$.
A fighter jet is flying horizontally at a certain altitude with a speed of $200 \; ms ^{-1}$. When it passes directly overhead an anti-aircraft gun, bullet is fired from the gun, at an angle $\theta$ with the horizontal, to hit the jet. If the bullet speed is $400 \; m / s$, the value of $\theta$ will be $\dots \; {}^o$