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 $(g = 10\, ms^{-2}$)
${\theta _0} = {\cos ^{ - 1}}\,\left( {\frac{1}{{\sqrt 5 }}} \right)$ and ${v_0} = \frac{5}{3}\,m{s^{ - 1}}$
${\theta _0} = {\cos ^{ - 1}}\,\left( {\frac{2}{{\sqrt 5 }}} \right)$ and ${v_0} = \frac{3}{5}\,m{s^{ - 1}}$
${\theta _0} = {\sin ^{ - 1}}\,\left( {\frac{2}{{\sqrt 5 }}} \right)$ and ${v_0} = \frac{3}{5}\,m{s^{ - 1}}$
${\theta _0} = {\sin ^{ - 1}}\,\left( {\frac{1}{{\sqrt 5 }}} \right)$ and ${v_0} = \frac{5}{3}\,m{s^{ - 1}}$
A projectile is thrown with an initial velocity of $(a \hat{ i }+b \hat{ j }) ms ^{-1}$. If the range of the projectile is twice the maximum height reached by it, then
A particle is projected with speed $u$ at angle $\theta$ with horizontal from ground. If it is at same height from ground at time $t_1$ and $t_2$, then its average velocity in time interval $t_1$ to $t_2$ is .........
A ball is thrown at an angle $\theta $ and another ball is thrown at an angle $(90^o -\theta )$ with the horizontal from the same point with same speed $40\,ms^{-1}$. The second ball reaches $50\,m$ higher than the first ball. Find their individual heights?
Which one of the following statements is not true about the motion of a projectile?
An object is projected from ground with speed $u$ at angle $\theta$ with horizontal. the radius of curvature of its trajectory at maximum height from ground is ..........