The velocity at the maximum height of a projectile is half its initial velocity of projection. Find its range on the horizontal plane. If $u=20{\text{ms}}^{-1}$. (Take $g=10{\text{m/s}}^2$)

Q. The velocity at the maximum height of a projectile is half its initial velocity of projection. Find its range on the horizontal plane. If $u=20{\text{ms}}^{-1}$. (Take $g=10{\text{m/s}}^2$)

Q. The velocity at the maximum height of a projectile is $\sqrt{3}/2$ times of its initial velocity of projection which is $u=20{\text{ms}}^{-1}$. Find the range of projectile on the horizontal plane.
(Take $g=10{\text{m/s}}^2$)

Q. A bob attached to a light string of length $10\text{m}$ is given an initial velocity of $20\text{m/s}$ at the bottom-most point to perform vertical circular motion. What will be the velocity of bob just before slacking of string?
(Take $g=10m/s^2$)

Q. A particle is projected with velocity of $u=30\hat{i}+40\hat{j}$. Its velocity after $2$ seconds is
Take $(g=10m/s^2)$

Q. A particle is projected from the bottom of an inclined plane of inclination ${30}^{\circ }$ (with the horizontal) with speed $40\text{m/s}$ at an angle ${60}^{\circ }$ with the horizontal. The speed of the particle when its velocity vector is parallel to inclined plane is $(g=10{\text{m/s}}^2)$