At the time of projection, the particle's speed is $u$ and the particle's speed at the

$\Delta u = u – u \cos \theta$

Now, the initial velocity is,

$\overrightarrow{ u }= u \cos \theta \hat{ i }+ u \sin \theta \hat{ j }$

and the final velocity (at highest point) is,

$\overrightarrow{ v }= u \cos \theta \hat{i}$

Therefore, the change in velocity is,

$\Delta \overrightarrow{ v }=\overrightarrow{ u }-\overrightarrow{ v }=u \cos \theta \hat{ i }+u \sin \theta \hat{ j }- u \cos \theta \hat{ i }=u \sin \theta \hat{ j }$

$\Rightarrow|\Delta \overrightarrow{ v }|=\operatorname{usin} \theta$