Question

a boy travels d distance towards north with speed v1 and then takes a right turn towards east to travel same distance d with speed v2. find average velocity of entire journey??
right ans is 2v1v2/v1+v2​

Answer 1

The boy travels d distance towards north with speed v1.

so, time taken by the boy to cover d distance towards north , t1 = d/v1

now the boy takes a right turn toward east to travel same distance d with speed v2.

so, time taken to travel d distance towards east , t2 = d/v2

displacement in vector form, s = d i + d j

so, magnitude of displacement, |s| = √{d² + d²} = √2d

then, average velocity = displacement/time taken

= √2d/{d/v1 + d/v2}

= √2v1v2/(v1 + v2)

hence, average velocity of entire journey is √2v1v2/(v1 + v2)