Motion in a Plane PYQs

The $x$ and $y$ coordinates of the particle at any time are $x = 5t - 2t^2$ and $y = 10t$ respectively, where $x$ and $y$ are in meters and $t$ in seconds. The acceleration of the particle at $t = 2\ \text{s}$ is

An airplane is moving horizontally with speed 100 m/s at a height of 2000 m from the ground. A small object is detached from it and strikes the ground. Calculate the angle from the vertical with which it strikes the ground.

Two boys are standing at the ends A and B of a ground, where $AB = a$. The boy at B starts running in a direction perpendicular to $AB$ with velocity $v_1$. The boy at A starts running simultaneously with velocity $v$ and catches the other boy in a time $t$. Then $t$ is: