Question

A particle is projected from ground with initial speed $u$ at angle $\theta$ with horizontal. If air friction is absent, then the average velocity of complete motion will be:

• A. $u\cos \theta$
• B. $u\sin \theta$
• C. $2u\cos \theta$
• D. $2u\sin \theta$

Answer 1

The correct option is A $u\cos \theta$

To know the average time traveled from being one point of height to other which is same from the ground determines the parabolic shapes of projectile.

Hence given as speed u at angle \theta and time as $t_1$ and $t_1$ . Horizontal component of the velocity be u cos \theta and the total displacement in travelling from $t_1$ to $t_2$ be$,$

$u\cos \theta \times \left(t_1-t_2\right)$

=> Total time taken be$(t_1-t_2)$

Therefore the average velocity be$,$

$V_a=\frac{Totaldisplacement}{Totaltime}$

$=V_a=u\cos \theta \times \frac{\left(t_1-t_2\right)}{\left(t_1-t_2\right)}=u\cos \theta$

Hence,

option $\left(A\right)$ is correct answer.