A cannon on a level plane is aimed at an angle $heta$ above the horizontal and a shell is fired with muzzle velocity ${v_0}$ towards a cliff D distance away. The height at which the cannon strikes the cliff is given by

A body is projected with a speed u m/s at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $\frac{3}{4}\;th$ of the initial energy. The values of β is

Two stones are projected with same velocity v at an angle $heta$ and $\left( {90^\circ - {\rm{heta }}} \right)$. If H and ${H_1}$ are greatest heights in the two paths, what is the relation between R,H and ${H_1}$?

An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth’s surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling

A body is projected with speed $v\;{\rm{m}}{{\rm{s}}^{ - 1}}$ at angle $heta$. The kinetic energy at the highest point is half of the initial kinetic energy. The value of $heta$ is

Two bodies are projected with the same velocity. If one is projected at an angle of ${30^0}$ and the other at an angle of ${60^0}$ to the horizontal, the ratio of the maximum heights reached is

A projectile moves from the ground such that its horizontal displacement is x=Kt and vertical displacement is $y = Kt\left( {1 - \alpha t} \right)$ , where K and α are constants and t is time. Find out total time of flight (T) and maximum height attained $\left( {{{\rm{Y}}_{{\rm{max}}}}} \right)$ its

A man can throw a stone to a maximum distance of 80 m. The maximum height to which it will rise in metre, is

Two projectiles thrown from the same point at angles ${60^0}$ and ${30^0}$ with the horizontal attain the same height. The ratio of their initial velocities is

An aeroplane moving horizontally with a speed of 720 km/h drops a food pocket, while flying at a height of 396.9 m. The time taken by a food pocket to reach the ground and its horizontal range is (Take g=$9.8\;m/{\sec ^2}\;)$

A ball is projected up an incline of ${30^0}$ with a velocity of $30{\rm{\;m}}{{\rm{s}}^{ - 1}}$ at an angle of ${30^0}$ with reference to the inclined plane from the bottom of the inclined plane. If ${\rm{g}} = 10{\rm{m}}{{\rm{s}}^{ - 2}}$, then the range on the inclined plane is