Two objects are thrown up at angles of $45^{\circ}$ and $60^{\circ}$ respectively, with the horizontal. If both objects attain same vertical height, then the ratio of magnitude of velocities with which these are projected is .........

A ball is projected with kinetic energy $E$ at an angle of ${45^o}$ to the horizontal. At the highest point during its flight, its kinetic energy will be

A bullet is fired from a gun at the speed of $280\,ms ^{-1}$ in the direction $30^{\circ}$ above the horizontal. The maximum height attained by the bullet is $........\,m$ $\left(g=9.8\,ms ^{-2}, \sin 30^{\circ}=0.5\right):-$

A projectile has initially the same horizontal velocity as it would acquire if it had moved from rest with uniform acceleration of $3\, ms^{-2}$ for $ 0.5\, minutes$. If the maximum height reached by it is $80\, m$, then the angle of projection is (Take $g = 10\, ms^{-2}$)

A player kicks a football with an initial speed of $25\, {ms}^{-1}$ at an angle of $45^{\circ}$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g $=10 \,{ms}^{-2}$ )

A ball is thrown at different angles with the same speed $u$ and from the same point. It has the same range in both cases. If $y_1$ and $y_2$ be the heights attained in the two cases, then $y_1+y_2$ equals to