$A$ ball of mass $1 \; kg$ is thrown vertically upwards and returns to the ground after $3 \; s$. Another ball,thrown at $60^{\circ}$ with the vertical,also stays in the air for the same time before it touches the ground. The ratio of the two maximum heights reached is:

$A$ particle is moving in a circle:

$A$ boy ties a stone of mass $100 \,g$ to the end of a $2 \,m$ long string and whirls it around in a horizontal plane. The string can withstand a maximum tension of $80 \,N$. If the maximum speed with which the stone can revolve is $\frac{K}{\pi} \,rev/min$,find the value of $K$. (Assume the string is massless and unstretchable)

$A$ boy throws a ball with a velocity $V_0$ at an angle $\alpha$ to the ground. At the same time,he starts running with a uniform velocity to catch the ball before it hits the ground. To achieve this,he should run with a velocity of

Two cars $S_1$ and $S_2$ are moving in coplanar concentric circular tracks in the opposite sense with the periods of revolution $3 \, min$ and $24 \, min$,respectively. At time $t = 0$,the cars are farthest apart. Then,the two cars will be

$A$ block of mass $5\,kg$ is moving horizontally at a speed of $1.5\,m/s$. $A$ perpendicular force of $5\,N$ acts on it for $4\,s$. What will be the distance of the block from the point where the force started acting?