Dynamics Questions

A velocity $V=\frac{1}{4}\text{m/s}$ is resolved into two components along $OA$ and $OB$ making angles $30^{\circ }$ and $45^{\circ }$ respectively with the given velocity. Then the component along $OB$ is

If $t_1$ and $t_2$ are the times of flight of two particles having the same initial velocity $u$ and range $R$ on the horizontal, then $t_1^2+t_2^2$ is equal to

A particle moves towards east from a point $A$ to a point $B$ at the rate of $4\text{km/h}$ and then towards north from $B$ to $C$ at the rate of $5\text{km/h}.$ If $AB=12\text{km}$ and $BC=5\text{km},$ then its average speed for its journey from $A$ to $C$ and resultant average velocity direct from $A$ to $C$ are respectively

A lizard, at an initial distance of $21\text{ cm}$ behind an insect, moves from rest with an acceleration of $2{\text{ cm/s}}^2$ and pursues the insect which is crawling uniformly along a straight line at a speed of $20\text{ cm/s}$. Then the lizard will catch the insect after:

Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f^{\prime }$ respectively. If $A$ takes $m\text{ sec.}$ more than $B$ and describes $n$ units more than $B$ in acquiring the same speed then:

A particle is projected from a point $O$ with velocity $u$ at an angle of $60^{\circ }$ with the horizontal. When it is moving in a direction at right angles to its direction at $O$, its velocity then is given by: