Motion In Two Dimensions

The speed of a swimmer in still water is $20ms^{-1}.$ The speed of river water is $10ms^{-1}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle…

Two stones of masses $m$ and $2m$ are whirled in horizontal circles, the heavier one in radius $\frac{r}{2}$ and the lighter one in radius $r$. The tangential speed of lighter stone is $n$ times that of the tangential…

The speed of a swimmer in still water is \$20ms^{-1}.$ The speed of river water is \$10ms^{-1}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the…

A person sitting in the ground floor of a building notices through the window, of height \$1.5m,$ a ball dropped from the roof of the building crosses the window in \$0.1s.$ What is the velocity of the ball when it is…

When an object is shot from the bottom of a long smooth inclined plane kept at an angle \$60^{\circ}$ with horizontal, it can travel a distance \$x_{1}$ along the plane. But, when the inclination is decreased to…

A projectile is fired from the surface of the earth with a velocity of \$5ms^{-1}$ and angle \$\theta$ with the horizontal. Another projectile fired from another planet with a velocity of \$3ms^{-1}$ at the same angle…

A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega$ rpm. The tension in the string is $T$. If speed becomes $2 \omega$ while keeping the same radius, the tension in the string…

A particle moving with uniform speed in a circular path maintains:

A constant torque of $100 \mathrm{~N} \mathrm{~m}$ turns a wheel of moment of inertia $300 \mathrm{~kg} \mathrm{~m}^2$ about an axis passing through its centre. Starting from rest, its angular velocity after $3…

A particle is executing uniform circular motion with velocity $\vec{v}$ and acceleration $\vec{a}$. Which of the following is true?

A ball is projected from point $A$ with velocity $20 \mathrm{~m} \mathrm{~s}^{-1}$ at an angle $60^{\circ}$ to the horizontal direction. At the highest point $B$ of the path (as shown in figure), the velocity $v…

A bullet is fired from a gun at the speed of\$280ms^{-1}$ in the direction \$30^{\circ}$ above the horizontal. The maximum height attained by the bullet is (\$g=9.8ms^{-2},$ \$sin30^{\circ}=0.5$):