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…

A particle is projected at $60^{\circ}$ to the horizontal with a kinetic energy $\mathrm{K}$. The kinetic energy at the highest point is

Given below are two statements: one is labelled asAssertion $A$and the other is labelled asReason$R.$ Assertion A:When a body is projected at an angle $45^{\circ},$its range is maximum. Reason R:For maximum range, the…

A river is flowing from west to east direction with speed of $9 \mathrm{~km} \mathrm{~h}^{-1}$. If a boat capable of moving at a maximum speed of $27 \mathrm{~km} \mathrm{~h}^{-1}$ in still water, crosses the river in…

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at$x=+2m$, its velocity is$-4j^ms^{-1}$. The object’s velocity$(v)$and…

A boy throws a ball into air at $45^{\circ}$ from the horizontal to land it on a roof of a building of height $H$. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of…

A particle of mass$m$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 its maximum…

If the radius of curvature of the path of two particles of same mass are in the ratio$3:4$, then in order to have constant centripetal force, their velocities will be in the ratio of:

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $9 \mathrm{~m}$ and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is…

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

Two projectiles are projected at$30^{\circ}$and $60^{\circ}$with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is: