$A$ projectile is fired with a speed $u$ at an angle $\theta$ with the horizontal. Its speed when its direction of motion makes an angle $\alpha$ with the horizontal is

$A$ helicopter is flying horizontally with a speed $v$ at an altitude $h$ and has to drop a food packet for a man on the ground. What is the distance of the helicopter from the man when the food packet is dropped?

The trajectory of a projectile,projected from the ground,is given by $y = x - \frac{x^2}{20}$,where $x$ and $y$ are measured in meters. The maximum height attained by the projectile will be $...........\,m$.

$A$ fighter jet is flying horizontally at a certain altitude with a speed of $200 \; m/s$. When it passes directly overhead an anti-aircraft gun,a bullet is fired from the gun at an angle $\theta$ with the horizontal to hit the jet. If the bullet speed is $400 \; m/s$,the value of $\theta$ will be $\dots \; ^\circ$.

$A$ projectile is thrown with a velocity of $10 \sqrt{2} \ m/s$ at an angle of $45^{\circ}$ with the horizontal. The time interval between the moments when the speed is $\sqrt{125} \ m/s$ is $(g = 10 \ m/s^2)$. (in $s$)

$A$ projectile is projected at $30^{\circ}$ from horizontal with initial velocity $40\,m/s$. The velocity of the projectile at $t = 2\,s$ from the start will be $........$ (Given $g = 10\,m/s^2$)