$A$ particle of mass $M$ is moving in a horizontal circle of radius $R$ with uniform speed $v$. When the particle moves from one point to a diametrically opposite point,its

Two boys conducted experiments on projectile motion with a stopwatch and noted some readings. As one boy throws a stone into the air at an angle with the horizontal,the other boy observes that after $4 \ s$,the stone is moving at an angle of $30^{\circ}$ to the horizontal,and after another $2 \ s$,it is traveling horizontally. The magnitude of the initial velocity of the stone is (Acceleration due to gravity,$g = 10 \ ms^{-2}$):

$A$ body of mass $0.5 \,kg$ is projected under gravity with a speed of $98 \,m/s$ at an angle of $30^\circ$ with the horizontal. The change in momentum (in magnitude) of the body is ......... $N-s$.

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? $(g = 10 \, m/s^2)$

At a given instant of time, the position vector of a particle moving in a circle with a velocity $\vec{v} = 3 \hat{i} - 4 \hat{j} + 5 \hat{k}$ is $\vec{r} = \hat{i} + 9 \hat{j} - 8 \hat{k}$. Its angular velocity $\vec{\omega}$ at that time is:

The velocities of two particles $A$ and $B$,separated by a distance of $20 \ m$,are as shown in the figure. Find the angular velocity of $B$ with respect to $A$ in $rad/s$.