A particle is projected from the ground with an initial speed $\upsilon $ at an angle $\theta $ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is
$\frac{\upsilon }{2}\sqrt {1 + 2\,\,{{\cos }^{2\,}}\theta } $
$\frac{\upsilon }{2}\sqrt {1 + {{\cos }^{2\,}}\theta } $
$\frac{\upsilon }{2}\sqrt {1 + 3\,\,{{\cos }^{2\,}}\theta } $
$\upsilon \,\cos \,\theta $
A ball is projected from the ground with a speed $15 \,ms ^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then $tan\,\theta$ will be equal to
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 particle is thrown with a velocity of $u \,m / s$. It passes $A$ and $B$ as shown in figure at time $t_1=1 \,s$ and $t_2=3 \,s$. The value of $u$ is ....... $m / s$ $\left(g=10 \,m / s ^2\right)$
A boy playing on the roof of a $10\, m$ high building throws a ball with a speed of $10\, m/s$ at an angle $30^o$ with the horizontal. ........ $m$ far from the throwing point will the ball be at the height of $10\, m$ from the ground . $(g \,= \,10 m/s^2, \,sin \,30^o \,= \,\frac{1}{2}$, $\cos \,{30^o}\, = \,\frac{{\sqrt 3 }}{2}$)
Two bodies are thrown up at angles of $45^o $ and $60^o $, respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is