A man on a rectilinearly moving cart, facing the direction of motion, throws a ball straight up with respect to himself
The ball will always return to him
The ball will fall behind him if the cart moves with some acceleration
The ball will return to him if the cart moves with constant velocity
Both $(B)$ and $(C)$
A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector? The rotation of a body can be specified by the direction of the axis of rotation, and the angle of rotation about the axis. Does that make any rotation a vector?
The velocity of a body at time $ t = 0$ is $10\sqrt 2 \,m/s$ in the north-east direction and it is moving with an acceleration of $ 2 \,m/s^{2}$ directed towards the south. The magnitude and direction of the velocity of the body after $5\, sec$ will be
Starting from the origin at time $t=0,$ with initial velocity $5 \hat{ j }\, ms ^{-1},$ a particle moves in the $x-y$ plane with a constant acceleration of $(10 \hat{ i }+4 \hat{ j })\, ms ^{-2}$. At time $t$, its coordinates are $\left(20\, m , y _{0}\, m \right) .$ The values of $t$ and $y _{0},$ are respectively
If vectors $\overrightarrow {A} = cos\omega t\hat i + sin\omega t\hat j$ and $\overrightarrow {B} = cos\frac{{\omega t}}{2}\hat i + sin\frac{{\omega t}}{2}\hat j$ are functions of time, then the value of $t$ at which they are orthogonal to each other is