$A$ particle is projected from the horizontal making an angle of $53^{\circ}$ with an initial velocity of $100\,m/s$. The time taken by the particle to make an angle of $45^{\circ}$ with the horizontal is $.........\,s$.

$A$ particle at a distance of $1 \ m$ from the origin starts moving,such that $dr/d\theta = r$,where $r$ and $\theta$ are polar coordinates. Then,the angle between the resultant velocity and the tangential velocity is

The hour hand of a clock is $6\,cm$ long. The magnitude of the displacement of the tip of the hour hand between $1:00\,PM$ and $5:00\,PM$ is:

$A$ body of mass $1\, kg$ tied to one end of a string is revolved in a horizontal circle of radius $0.1\, m$ with a speed of $3$ revolutions per second. Assuming the effect of gravity is negligible,the linear velocity,acceleration,and tension in the string will be:

$A$ cricketer can throw a ball to a maximum horizontal distance of $100\,m$. With the same speed,how high above the ground can the cricketer throw the same ball (in $,m$)?

Two particles are projected simultaneously in the same vertical plane,from the same point on the ground,with the same speeds but at different angles $( < 90^o )$ to the horizontal. The path followed by one,as seen by the other,is