Two identical balls are projected, one vertically up and the other at an angle of ${30}^{\circ }$ with the horizontal, with same initial speed. The potential energy at the highest point is in the ratio

Q. A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected at an angle of ${60}^{\circ }$ with the vertical with the same initial speed. At the highest point, the ratio of their potential energies will be

Q. Two balls are projected at an angle $\theta$ and (90${}^{\circ }$ - $\theta$) to the horizontal with the same speed. The ratio of their maximum vertical heights is

Q. Two identical balls $P$ and $Q$ are projected with same speeds in vertical plane from same point $O$ with making projection angles with horizontal ${30}^{\circ }$ and ${60}^{\circ }$, respectively and they fall directly on plane $AB$ at points $P^{\prime }$ and $Q^{\prime }$ respectively. Which of the following statement is true about distance as given in options?

Q. A particle of mass $1\text{kg}$ is projected from the ground with an initial speed $u$ at an angle ${60}^{\circ }$ with the horizontal. At the highest point of its trajectory, it makes a complete inelastic collision with another identical particle, which was thrown vertically upwards from the ground with the same initial speed $u$. The angle that the composite system makes with the horizontal just after collision in degrees is .