At the same instant, two boys throw balls $A$ and $B$ from a window with speeds $v_0$ and $k{v}_0$, respectively, where $k$ is constant. They collide in air at time $t$. Which of the following option(s) is/are correct?

A cart is moved horizontally with a constant velocity of $4 {\mathrm{ms}}^{-1}$. A ball is thrown from it with a velocity of $4 {\mathrm{ms}}^{-1}$ and at an angle $\theta$ with the horizontal with respect to the cart. Assume the height of the cart is very small, so that the motion of the ball is assumed to be a ground-to-ground projectile. Horizontal range of the ball with respect to the ground is $R_1$ and that with respect to the cart is $R_2$. Then

A bead is free to slide down on a smooth wire rightly stretched between points $A$ and $B$ on a vertical circle of radius $10 \mathrm{m}$. Find the time taken by the bead to reach the point $B$, if the bead slides from rest from the highest point $A$ on the circle.