A projectile thrown with velocity $v$ making angle $\theta$ with vertical gains maximum height $H$ in the time for which the projectile remains in air, the time period is
$\sqrt {H\,\cos \,\theta /g} $
$\sqrt {2H\,\cos \,\theta /g} $
$\sqrt {4H/g} $
$\sqrt {8H/g} $
A bullet is fired from a gun at the speed of $280\,ms ^{-1}$ in the direction $30^{\circ}$ above the horizontal. The maximum height attained by the bullet is $........\,m$ $\left(g=9.8\,ms ^{-2}, \sin 30^{\circ}=0.5\right):-$
The trajectory of a projectile near the surface of the earth is given as$ y = 2x -9x^2$. If it were launched at an angle $\theta_0$ with speed $v_0$ then $(g = 10\, ms^{-2}$)
The equation of motion of a projectile is $y=12 x-\frac{3}{4} x^2$ $..........\,m$ is the range of the projectile.
Two bodies are projected from ground with same speeds $40 ms ^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60^{\circ}$, with horizontal then sum of the maximum heights, attained by the two projectiles, is $.......m$. (Given $g =10 ms ^{-2}$ )
A projectile is thrown upward with a velocity $v_0$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is