Question

A particle is thrown with speed $u$ at an angle of projection $\theta$ with horizontal as shown in figure. Choose the correct statement.

• A. Average velocity between $O$ and $D$ is $u\cos \theta$
• B. Average velocity between $A$ and $C$ is $u\cos \theta$
• C. Dot product of vertical components of velocities at $A$ and $C$ is negative.
• D. All of these

Answer 1

The correct option is D All of these

Between two points of equal height, the displacement will only be along the horizontal direction.$\therefore x=u_x\times △t$ (where $x$ is displacement and $△t$ is the time interval between two points of equal height.)
$\Rightarrow$ Average velocity $=\frac{u_x\times △t}{△t}=u\cos \theta$
$\therefore$ Options (a) and (b) are correct.
As points $A$ and $C$ are at same height from the ground so, the magnitude of velocity will be same at both these points.
At point $A$, the vertical component of velocity is in upward direction as the particle is moving upwards in that direction.
At point $C$, the vertical component of velocity is in downward direction as the particle is moving downwards in that direction.
As the vertical components of velocities at points $A$ and $C$ are in opposite direction to each other so their dot product is negative.