Question
Two cyclists start from the junction of two perpendicular roads, their velocities being $$3v$$ metres/minute and $$4v$$ metres/minute. The rate at which the two cyclists are separating is :
A.
$$\frac{7}{2}v\,{\text{m/min}}$$
B.
$$5v\,{\text{m/min}}$$
C.
$$v\,{\text{m/min}}$$
D.
none of these
Answer :
$$5v\,{\text{m/min}}$$
Solution :
At time $$t,$$ the distance $$z$$ between the cyclists is given by $${z^2} = {\left( {3vt} \right)^2} + {\left( {4vt} \right)^2}$$
$$\therefore \,\,z = 5vt\,\,\,\,\,\, \Rightarrow \frac{{dz}}{{dt}} = 5v$$