Question

A container of length $4\text{m}$, width $2\text{m}$ and height $3\text{m}$ is kept on a horizontal floor. A bee enters the container from a hole at bottom-most corner $\left(A\right)$ and comes out of the hole$\left(B\right)$ at diagonally opposite corner. If the displacement of bee is maximum when it comes out, what is its displacement ?

• A. $\sqrt{20}\text{m}$
• B. $\sqrt{29}\text{m}$
• C. $9\text{m}$
• D. $\sqrt{41}\text{m}$

Answer 1

The correct option is B $\sqrt{29}\text{m}$

It is given that bee enters from hole at bottom-most corner $A$
$\Rightarrow$Since its displacement is maximum, the displacement of bee will be along central diagonal or body diagonal $AB$ of the container.
From figure,
$AC=\sqrt{4^2+2^2}=\sqrt{20}\text{m}$
The triangle formed by body diagonal $AB$, face diagonal $AC$ and edge $BC$ is a right angled triangle$\left(\Delta ABC\right)$.
Applying pythagoras theorem,
$A{B}^2=A{C}^2+B{C}^2$
$\Rightarrow A{B}^2=20+9$
$\therefore AB=\sqrt{29}\text{m}$
It is the required displacement of the bee.