Motion In Two Dimensions

A girl standing on road holds her umbrella at $45^{\circ}$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2}\mathrm{km}h^{-1}$, the rain drops hit her head…

A small particle of mass $m$ is projected at an angle $\theta$ with the $\mathrm{x}$-axis with an initial velocity $\mathrm{v}_0$ in the $\mathrm{x}-\mathrm{y}$ plane as shown in the figure. At a time $t < \frac{v_0…

A small bob tied at one end of a thin string of length $1m$ is describing a vertical circle so that the maximum and minimum tension in the string is in the ratio $5:1$. The velocity of the bob at the highest position…

The water is filled up to a height of $12m$ in a tank having vertical sidewalls. A hole is made in one of the walls at a depth$h$ below the water level. The value of$h$ for which the emerging stream of water strikes the…

A particle of mass $m$is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r=\frac{L}{\sqrt{2}}$. The speed of particle will be :

A butterfly is flying with a velocity $4\sqrt{2}ms^{-1}$ in north-east direction. Wind is slowly blowing at $1ms^{-1}$ from north to south. The resultant displacement of the butterfly in $3$ seconds is:

A body is projected from the ground at an angle of $45^{\circ}$ with the horizontal. Its velocity after $2s$ is $20ms^{-1}$. The maximum height reached by the body during its motion is _____$m$. (use $g=10ms^{-2}$)

The initial speed of a projectile fired from ground is $u$. At the highest point during its motion, the speed of projectile is $\frac{\sqrt{3}}{2}u$. The time of flight of the projectile is:

A uniform cylinder of mass$M$and radius$R$is to be pulled over a step of height a$\left(a$

A projectile is launched at an angle $\alpha\,$with the horizontal with a velocity $20ms^{-1}$. After $10s$, its inclination with horizontal is $\beta\,$. The value of $\tan\,\beta\,$ will be :…

Two particles $A,B$ are moving on two concentric circles of radii $R_{1}$ and $R_{2}$ with equal angular speed $\omega\,.$ At $t=0,$ their positions and direction of motion are shown in the figure: The relative velocity…

A projectile fired at $30^{\circ}$ to the ground is observed to be at same height at time $3s$ and $5s$ after projection, during its flight. The speed of projection of the projectile is $ms^{-1}$. (Given $g=10ms^{-2}$)