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 objects are projected with the same velocity '$u$' but at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha + \beta = 90^{\circ}$,the ratio of the horizontal range of the first object to the $2^{\text{nd}}$ object will be:

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.

$A$ 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

$A$ 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?

$A$ body is projected at an angle of $45^{\circ}$ from a point on the ground at a distance of $30 \,m$ from the foot of a vertical pole of height $20 \,m$. The body just crosses the top of the pole and strikes the ground at a distance $s$ from the foot of the pole on the other side. Then, $s$ is: (in $\,m$)