Average velocity of a particle is projectile motion between its starting point and the highest point of its trajectory is : (projection speed = $u$, angle of projection from horizontal= $\theta$)
$u\,\, cos\theta$
$\frac{u}{2}\sqrt {1 + 3{{\cos }^2}\theta } $
$\frac{u}{2}\sqrt {2 + {{\cos }^2}\theta }$
$\frac{u}{2}\sqrt {1 + {{\cos }^2}\theta }$
A particle of mass $m$ is projected with a velocity $V$ making an angle of $45^o$ with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is
Two cars of masses $m_1$ & $m_2$ are moving along the circular paths of radius $r_1$ & $r_2$ respectively. Their speeds are such that they complete one round in same time. The ratio of angular speeds of two cars is
A body of mass $1 \,kg$ is projected from ground at an angle $30^{\circ}$ with horizontal on a level ground at a speed $50 \,m / s$. The magnitude of change in momentum of the body during its flight is ....... $kg ms ^{-1}$ $\left(g=10 \,m / s ^2\right)$
For a particle in uniform circular motion, the acceleration $\overrightarrow{ a }$ at any point $P ( R , \theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x\,-$axis and $v$ is uniform speed)
A body of mass $m\, kg$ is rotating in a vertical circle at the end of a string of length $r$ metre. The difference in the kinetic energy at the top and the bottom of the circle is