Question

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

Answer 1

Answer: 4

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