A ball is held in the position shown with string of length $1\,\, m$ just taut & then projected horizontally with a velocity of $3 \,\,m/s$. If the string becomes taut again when it is vertical, angle $\theta$ is given by  ........ $^o$

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. . . . .

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 man runs across the roof, top of a tall building and jumps horizontally with the hope of landing on the roof of the next building which is at a lower height than the first. If his speed is $9\, m/s$. the (horizontal) distance between the two buildings is $10\, m$ and the height difference is $9\, m$, will be able to land on the next building ? $($ Take $g = 10 \,m/s^2)$

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 bomber plane moves horizontally with a speed of $500\, m/s$ and a bomb released from it, strikes the ground in $10\, sec$. Angle at which it strikes the ground will be $(g = 10\,\,m/{s^2})$