Motion In Two Dimensions

A rigid body rotates about a fixed axis with variable angular velocity equal to $\alpha-\beta t$, at the time $t$, where $\alpha, \beta$ are constants. The angle through which it rotates before it stops is

A projectile is projected with velocity of $40 \mathrm{~m} / \mathrm{s}$ at an angle $\theta$ with the horizontal. If $R$ be the horizontal range covered by the projectile and after $t$ seconds, its inclination with…

A particle of mass $m$ is projected with a velocity ' $u$ ' making an angle of $30^{\circ}$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at…

The range of the projectile projected at an angle of $15^{\circ}$ with horizontal is 50 m . If the projectile is projected with same velocity at an angle of $45^{\circ}$ with horizontal, then its range will be :

A body is thrown with a velocity of 9.8 ms making an angle of $30^{\circ}$ with the horizontal. It will hit the ground after a time

A projectile is projected at $30^{\circ}$ from horizontal with initial velocity $40 \mathrm{~ms}^{-1}$. The velocity of the projectile at $\mathrm{t}=2 \mathrm{~s}$ from the start will be: (Given $\mathrm{g}=10…

A gun fires two bullets at $60^{\circ}$ and $30^{\circ}$ with horizontal. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio of

A wheel is rotating at $900 \mathrm{r}$.p.m. about its axis. When power is cut offit comes to rest in 1 minute. The angular retardation in $\mathrm{rad} / \mathrm{s}^{2}$ is

The equation of a projectile is $y=\sqrt{3} x-\frac{g x^{2}}{2}$ The angle of projection is given by

A projectile is given an initial velocity of $(\vec{i}+\sqrt{3} \vec{j}) m {s}^{-1},$ where $\vec{i}$ is along the ground and $\vec{j}$ is along the vertical. Then, the equation of the path of projectile is $[$Take,…

The horizontal range and maximum height attained by a projectile are $R$ and $H$ respectively. If a constant horizontal acceleration $a=\frac{g}{4}$ is imparted to the projectile due to wind, then its horizontal range…

At what angle $θ$ to the horizontal should an object is projected so that the maximum height reached is equal to the horizontal range?