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
$2\sqrt 3\ sec$
$\frac{5}{{\sqrt 2 }}\ sec$
$3\sqrt 2\ sec$
$2\sqrt 2\ sec$
Find time of flight of projectile thrown horizontally with speed $50 ms^{^{-1}}$ from a long inclined plane which makes an angle of $\theta = 45^o$ from horizontal ........ $\sec$
A projectile is thrown with a velocity of $10\,m / s$ at an angle of $60^{\circ}$ with horizontal. The interval between the moments when speed is $\sqrt{5 g}\,m / s$ is $..........\,s$ $\left(g=10\,m / s ^2\right)$.
Two particles are moving along two long straight lines, in the same plane, with the same speed $= 20 \,\,cm/s$. The angle between the two lines is $60^o$, and their intersection point is $O$. At a certain moment, the two particles are located at distances $3\,m$ and $4\,m$ from $O$, and are moving towards $O$. Subsequently, the shortest distance between them will be
In the given figure for a projectile
An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range $R$, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be $.......$ degree.