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

Ratio between maximum range and square of time of flight in projectile motion is

An object of mass 2 m is projected with a speed of $100{\rm{\;m}}{{\rm{s}}^{ - 1}}$ at angle ${\rm{heta }} = {\rm{si}}{{\rm{n}}^{ - 1}}\left( {\frac{3}{5}} \right)$ to the horizontal. At the highest point, the object breaks into pieces of same mass m and the first one comes to rest. The distance between the point of projection and the point of landing of the bigger piece (in metre) is $\left( {{\rm{given}},{\rm{\;}}g = 10{\rm{\;m}}{{\rm{s}}^{ - 2}}} \right)$

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

The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. The percentage increase in the horizontal range will be

For a projectile, the ratio of maximum height reached to the square of flight time is $\left( {g = 10\;m{s^{ - 2}}} \right)$

Two projectile are thrown with the same initial velocity at angles ${\rm{\alpha }}$ and $\left( {90^\circ - {\rm{\alpha }}} \right)$ with the horizontal. The maximum heights attained by them are ${h_1}\,and\,{h_2}$ respectively. Then $\frac{{{h_1}}}{{{h_2}}}$ is equal to

A stone is projected with a velocity $20\sqrt 2 {\rm{m}}{{\rm{s}}^{ - 1}}$ at an angle of ${45^0}$ to the horizontal. The average velocity of stone during its motion from starting point to its maximum height is $\left( {{\rm{g}} = 10{\rm{m}}{{\rm{s}}^{ - 2}}} \right)$

Two bodies are projected from ground with equal speed $20\;{\rm{m}}{{\rm{s}}^{ - 1}}$ from the same position in the same vertical plane to have equal range but at different angles above the horizontal. If one of the angle is ${30^0}$ the sum of their maximum heights is $\left( {{\rm{assume\;}}g = \;10\;{\rm{m}}{{\rm{s}}^{ - 2}}} \right)$

A projectile is thrown at angle $\beta$ with vertical. It reaches a maximum height H. The time taken to reach the highest point of its path is

The speed of projection of a projectile is increased by 10%, without changing the angel of projection. The percentage increase in the range will be