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
$2\sqrt 3\ sec$
$\frac{5}{{\sqrt 2 }}\ sec$
$3\sqrt 2\ sec$
$2\sqrt 2\ sec$
An insect trapped in a circular groove of radius $12 \;cm$ moves along the groove steadily and completes $7$ revolutions in $100\; s$.
$(a)$ What is the angular speed, and the linear speed of the motion?
$(b)$ Is the acceleration vector a constant vector ? What is its magnitude ?
Two projectiles of same mass and with same velocity are thrown at an angle $60^o$ and $30^o$ with the horizontal, then which quantity will remain same
A gun can fire shells with maximum speed $v_0$ and the maximum horizontal range that can be achieved is $R_{max} = \frac {v_0^2}{g}$. If a target farther away by distance $\Delta x$ (beyond $R$) has to be hit with the same gun, show that it could be achieved by raising the gun to a height at least $h = \Delta x\,\left[ {1 + \frac{{\Delta x}}{R}} \right]$.
A particle is projected vertically upwards from $O$ with velocity $v$ and a second particle is projected at the same instant from $P$ (at a height h above $O$) with velocity $v$ at an angle of projection $\theta$ . The time when the distance between them is minimum is
A person is standing on an open car moving with a constant velocity of $30\,\,m/s$ on a straight horizontal road. The man throws a ball in the vertically upward direction and it returns to the person after the car has moved $240\,\,m.$ The speed and the angle of projection