A projectile is thrown at an angle $\theta$ with the horizontal and its range is $R_1$. It is then thrown at an angle $\theta$ with vertical and the range is $R_2$, then

A fighter plane is flying horizontally at a height of $250\  m$ from ground with constant velocity of $500\  m/s$. It passes exactly over a cannon which can fire a shell at any time in any direction with a speed of  $100\  m/s$. Find the duration of time  for which the plane is in danger of being hit by a cannon shell

A particle is projected from the ground with velocity $u$ at angle $\theta$ with horizontal. The horizontal range, maximum height and time of flight are $R, H$ and $T$ respectively. They are given by $R = \frac{{{u^2}\sin 2\theta }}{g}$, $H = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}$ and $T = \frac{{2u\sin \theta }}{g}$  Now keeping $u $ as fixed, $\theta$ is varied from $30^o$ to $60^o$. Then,

What is range of the projectile particle ? Give velocity of projectile particle at maximum height.

A projectile is thrown with speed $40 \,ms ^{-1}$ at angle $\theta$ from horizontal. It is found that projectile is at same height at $1 \,s$ and $3 \,s$. What is the angle of projection?

For a given velocity, a projectile has the same range $R$ for two angles of projection if $t_1$ and $t_2$ are the times of flight in the two cases then