$A$ bullet fired from a gun falls at a distance half of its maximum range. The angle of projection of the bullet is (in $^{\circ}$)

If a stone projected from the ground takes $4 \, s$ to reach the topmost point of its trajectory,then the time of flight is .......... $s$.

Three balls of same masses are projected with equal speeds at angles $15^{\circ}, 45^{\circ}$,and $75^{\circ}$. If their ranges are $R_1, R_2$,and $R_3$ respectively,then:

What do you mean by projectile motion and projectile particle? Find the value of the position of a projectile particle at any instant of time.

$A$ missile is fired for maximum range at your town from a place $100 \, km$ away from you. If the missile is first detected at its half-way point,how much warning time will you have? (Take $g = 10 \, m/s^2$). What was the speed of the missile when it was detected?

$A$ projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$. When the acceleration due to gravity is $g$,the range of the projectile is $d$. If at the highest point in its trajectory,the projectile enters a different region where the effective acceleration due to gravity is $g^{\prime}=\frac{g}{0.81}$,then the new range is $d^{\prime}=n d$. The value of $n$ is. . . . .