Two objects are projected with same velocity ' $u$ ' however at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha+\beta=90^{\circ}$, the ratio of horizontal range of the first object to the $2^{\text {nd }}$ object will be :

A body is projected at $t = 0$ with a velocity $10\,ms^{-1}$ at an angle of $60^o$ with the horizontal. The radius of curvature of its trajectory at $t=1\,s$ is $R.$ Neglecting air resistance and taking acceleration due to gravity $g = 10\,ms^{-2},$ the radius of $R$ is   ........ $m$

A projectile is thrown in the upward direction making an angle of $60^o$ with the horizontal direction with a velocity of $150\, ms^{-1}$. Then the time after which its inclination with the horizontal is $45^o$ is

An object is projected from ground with speed $u$ at angle $\theta$ with horizontal. the radius of curvature of its trajectory at maximum height from ground is ..........

Two projectile thrown at $30^{\circ}$ and $45^{\circ}$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

A body is projected at an angle $\theta $ with horizontal, another body is projected with the same speed at an angle $\theta $ with the vertical then the ratio of the maximum height is