What is the path followed by a moving body, on which a constant force acts in a direction other than initial velocity (i.e. excluding parallel and antiparallel direction)?

A projectile is projected with velocity of $25\, m / s$ at an angle $\theta$ with the horizontal. After t seconds its inclination with horizontal becomes zero. If $R$ represents horizontal range of the projectile, the value of $\theta$ will be : [use $g =10 m / s ^{2}$ ]

The equation of a projectile is $y =\sqrt{3} x -\frac{ gx ^2}{2}$ the angle of projection is

A particle of mass $100\,g$ is projected at time $t =0$ with a speed $20\,ms ^{-1}$ at an angle $45^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t=2\,s$ is found to be $\sqrt{ K }\,kg\,m ^2 / s$. The value of $K$ is $............$ $\left(\right.$ Take $\left.g =10\,ms ^{-2}\right)$

A bullet fired at an angle of $30^o$ with the horizontal hits the ground $3.0\; km$ away. By adjusting its angle of projection, can one hope to hit a target $5.0\; km$ away ? Assume the muzzle speed to be fixed, and neglect air resistance.

Range of a bullet fired at $45^o$ to horizontal is $980m$. If the bullet is fired at same  angle from a car travelling horizontally at $18\, km/hr$ towards target then range will be  increased by :-