Question

An ant is at the corner of a cubical room of side $a$. The ant can move with a constant speed $u$. The minimum time taken by the ant to reach the farthest corner of the cube is

• A. $\frac{3a}{u}$
• B. $\frac{\sqrt{3}a}{u}$
• C. $\frac{\sqrt{5}a}{u}$
• D. $\frac{(\sqrt{2}+1)a}{u}$

Answer 1

The correct option is D $\frac{(\sqrt{2}+1)a}{u}$

Open the faces of the cube, so that they are projected on a plane and calculate the shortest distance, $d$, between the two points.
We get the shortest distance as $a+\sqrt{2}a$
Thus, we get the minimum time as $\frac{a+\sqrt{2}a}{u}$