Two identical bodies, projected with the same speed at two different angles cover the same horizontal range $R$. If the time of flight of these bodies are 5 s and 10 s , respectively, then the value of $R$ is

$\_\_\_\_$ m.  (Take $g=10 \mathrm{~m} / \mathrm{s}^2$ )

At $t=0$, a body of mass 100 g starts moving under the influence of a force $(5 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}) \mathrm{N} \cdot$ After 2 s its position is $(2 x \hat{\mathrm{i}}+5 y \hat{\mathrm{j}}) \mathrm{m}$. The ratio $x: y$ is $\_\_\_\_$ .

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24 t$ and $43.6 t-4.9 t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $t=2 \mathrm{~s}$ is $\_\_\_\_$ .

The two projectiles are projected with the same initial velocities at the $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their ranges is $1: x$. The value of $x$ is