$A$ projectile is thrown with an initial velocity of $10 \ m/s$ at an angle $\alpha$ with the horizontal. It has a range of $5 \ m$. Taking $g = 10 \ m/s^2$ and neglecting air resistance, what will be the estimated value of $\alpha$ (in $^{\circ}$)?

Assertion $(A)$: The range of a projectile is maximum when the angle of projection is $45^{\circ}$.
Reason $(R)$: The range of a projectile depends only on the angle of projection.

$A$ stone is projected in air. Its time of flight is $3\,s$ and range is $150\,m$. The maximum height reached by the stone is $......\,m$ $\left(g=10\,m/s^2\right)$.

Two projectiles,one fired from the surface of the Earth with velocity $10 \, m/s$ and the other fired from the surface of another planet with initial speed $5 \, m/s$,trace identical trajectories. The value of the acceleration due to gravity on the planet is ......... $m/s^2$.

$A$ 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 ......... $m$.

$A$ grasshopper can jump a maximum distance of $1.6 \; m$. It spends a negligible amount of time on the ground. How far can it go in $10 \; s$?