Question

$P$ is a point moving with constant speed $10\, m / s$ such that its velocity vector always maintains an angle $60^{\circ}$ with line $O P$ as shown in the figure $(O$ is a fixed point in space). The initial distance between $O$ and $P$ is $100\, m$. If after $5\, k$ seconds $P$ reaches $O$, then find the value of $k$.

Answer 1

Velocity of approach of $P$ and $O=-\frac{d x}{d t}=v \cos \,60^{\circ}=5\, m / s$
It can be seen that velocity of approach is always constant.
$\therefore P$ reaches $O$ after $\frac{100}{5}=20 \,s$.