Q: A particle of mass ‘m’ is projected at an angle θ to the horizontal with an initial velocity u. Find the work done by gravity during the time it reaches the highest point.

Sol: $\large \vec{F_y} = -mg\hat{j}$ ; $\large \vec{r_y} = H_{max} = \frac{u^2 sin^2 \theta}{2 g}\hat{j}$

$\large W = \vec{F_y}.\vec{r_y}$

$\large W = (-mg\hat{j}).(\frac{u^2 sin^2 \theta}{2 g}\hat{j})$

$\large = -\frac{1}{2}m u^2 sin^2\theta$