The position of a projectile launched from the origin at $t = 0$ is given by $\vec r = \left( {40\hat i + 50\hat j} \right)\,m$ at $t = 2\,s$. If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is (take $g = 10\, ms^{-2}$)
${\tan ^{ - 1}}\frac{2}{3}$
${\tan ^{ - 1}}\frac{3}{2}$
${\tan ^{ - 1}}\frac{7}{4}$
${\tan ^{ - 1}}\frac{4}{5}$
A particle projected from ground moves at angle $45^{\circ}$ with horizontal one second after projection and speed is minimum two seconds after the projection. The angle of projection of particle is [Neglect the effect of air resistance]
A bullet is fired from a cannon with velocity $500 \,m/s$. If the angle of projection is ${15^o}$ and $g = 10m/{s^2}$. Then the range is
A projectile projected at an angle ${30^o}$ from the horizontal has a range $2\upsilon ,\,\sqrt 2 \upsilon \,\,{\rm{ and}}\,{\rm{zero}}$. If the angle of projection at the same initial velocity be ${60^o}$, then the range will be
A ball of mass $1 \;kg$ is thrown vertically upwards and returns to the ground after $3\; seconds$. Another ball, thrown at $60^{\circ}$ with vertical also stays in air for the same time before it touches the ground. The ratio of the two heights are
A football player throws a ball with a velocity of $50$ metre/sec at an angle $30 $ degrees from the horizontal. The ball remains in the air for ...... $\sec$ $(g = 10\,m/{s^2})$