c
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,

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

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