In projectile motion, the modulus of rate of change of velocity

A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected with the same speed at an angle of $30^o$ with the horizontal. At the highest point, the ratio of their potential energies is

A particle is projected with a velocity of $30\,m / s$, at an angle of $\theta_0=\tan ^{-1}\left(\frac{3}{4}\right)$ After $1\,s$, the particle is moving at an angle $\theta$ to the horizontal, where $\tan \theta$ will be equal to $\left(g=10\,m / s ^2\right)$

Galileo, in his book Two new sciences, stated that “for elevations which exceed or fall short of $45^o$ by equal amounts, the ranges are equal”. Prove this statement.

A ball is thrown at different angles with the same speed $u$ and from the same point. It has the same range in both cases. If $y_1$ and $y_2$ be the heights attained in the two cases, then $y_1+y_2$ equals to

A particle covers $50\, m$ distance when projected with an initial speed. On the same surface it will cover a distance, when projected with double the initial speed ......... $m$