Question

if a boy starts from A and stops at d find the distance covered by the boy if possible displacement also ​

Answer 1

Answer:

distance = $\frac{3\pi r}{2}$

Displacement = $\sqrt{2} r$

Explanation:

body covered  $\frac{3}{4}$  part of triangle

we know that,

circumference = $2\pi r$

now,

        distance = $\frac{3}{4}$ × $2\pi r$

                      = $\frac{6\pi r}{4}$

                      = $\frac{3\pi r}{2}$

again,

displacement = shortest distance of point A and point D

we can see,

AOD is right isosceles triangle

so,

according to Pythagoras theorem

$(AD)^2 = (AO)^2+(OD)^2$

$AD =\sqrt{ (AO)^2+(OD)^2}$

$AD =\sqrt{ (r)^2+(r)^2}$                                   [ ∴  AO = r , OD = r]

$AD=\sqrt{2r^2}$

$AD=\sqrt{2} r$

Displacement = $\sqrt{2} r$