At the top of the trajectory of a projectile,the directions of its velocity and acceleration are

$A$ body is projected at $t = 0$ with a velocity $10\,ms^{-1}$ at an angle of $60^\circ$ with the horizontal. The radius of curvature of its trajectory at $t = 1\,s$ is $R$. Neglecting air resistance and taking acceleration due to gravity $g = 10\,ms^{-2}$,the value of $R$ is ........ $m$.

$A$ cricketer can throw a ball to a maximum horizontal distance of $100 \, m$. With the same effort,he throws the ball vertically upwards. The maximum height attained by the ball is ......... $m$.

$A$ particle moves in the $xy$ plane with a constant acceleration $g$ in the negative $y$-direction. Its equation of motion is $y = ax - bx^2$,where $a$ and $b$ are constants. Which of the following are correct?

The range of a projectile when launched at angle $\theta$ is same as when launched at angle $2\theta$. What is the value of $\theta$ (in $^{\circ}$)?

Two bodies are projected at angles $\theta$ and $(90^\circ - \theta)$ with the same initial velocity. Find the ratio of their times of flight.