Find the speed of the intersection point $O$ of the two wires if the wires start moving perpendicular to themselves with speed $v$ as shown in the figure.

$A$ particle is moving eastwards with a speed of $6 \, m/s$. After $6 \, s$,the particle is found to be moving with the same speed in a direction $60^{\circ}$ north of east. The magnitude of average acceleration in this interval of time is ....... $m/s^2$.

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is $R_0 = 10 \, m$. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $v = 20 \, m/s$,on a horizontal surface? $(g = 10 \, m/s^2)$

$A$ particle moves around a circular path of radius $r$ with uniform speed $V$. After moving half the circle,the average acceleration of the particle is

Two balls are projected from the same point simultaneously. The first ball is projected vertically upwards with velocity $u_1$ and the second ball at an angle of projection $60^{\circ}$ to the ground level with velocity $u_2$. Both the balls reach the ground simultaneously. The ratio of their velocities $u_1 : u_2$ is

$A$ projectile is thrown with velocity $v$ making an angle $\theta$ with the vertical. It reaches a maximum height $H$. The time of flight is: