In a sports competition,a javelin is thrown at an angle $45^{\circ}$,which recorded a range of $90 \,m$. The maximum height reached by the javelin is (Neglect air resistance and acceleration due to gravity $g = 10 \,ms^{-2}$)

$A$ particle is projected from the ground with an initial speed of $v$ at an angle of projection $\theta$. The average velocity of the particle between its time of projection and the time it reaches the highest point of its trajectory is

$A$ body is projected into a vertical $X-Y$ plane with the $X$-axis along the horizontal and the $Y$-axis along the vertical with an initial velocity $(10 \hat{i} + p \hat{j}) \ m/s$. If the maximum height reached by the body is $50 \%$ of its range,then the value of $p$ is:

Galileo,in his book $Two \text{ } new \text{ } sciences$,stated that "for elevations which exceed or fall short of $45^{\circ}$ by equal amounts,the ranges are equal". Prove this statement.

For a projectile, if $\alpha$ is the angle of projection, $R$ is the range, $h$ is the maximum height, and $T$ is the time of flight, then:

$A$ ball is dropped from a high tower,and another ball is thrown horizontally from the same position. Which ball will reach the ground first?