Question

A particle is fired with velocity $u$ making angle $\theta$ with the horizontal. What is the magnitude of change in velocity when it is at the highest point?

• A. $u\cos \theta$
• B. $u$
• C. $u\sin \theta$
• D. $(u\cos \theta -u)$

Answer 1

The correct option is C $u\sin \theta$

Let $\overrightarrow{v_i}$ and $\overrightarrow{v_H}$ be the initial velocity and velocity at highest point respectively. $\theta$ is the angle of projection.
$\overrightarrow{v_i}=u\cos \theta \hat{i}+u\sin \theta \hat{j}$
At the highest point of a projectile, the vertical component of velocity becomes $0$ and only horizontal component of velocity exists.
$\overrightarrow{v_H}=u\cos \theta \hat{i}$
Change in velocity can be given as,
$\overrightarrow{△v}=\overrightarrow{v_f}-\overrightarrow{v_i}=\overrightarrow{v_H}-\overrightarrow{v_i}$
$=-u\sin \theta \hat{j}$
$|\overrightarrow{△v}|=u\sin \theta$