Question

A boy moves 100m towards North then 70 my towards East then what is its displacement

Answer 1

Is there a formula for displacement?

Answer 2

Displacement is position vector
in this case it is

70 i + 100 j in x y coordinates where i is unit x and j is unit y vectors

its magnitude is sqrt (70^2 + 100^2)
it direction north of east is
tan theta = 100/70
the compass angle east of north is 90 -theta

Answer 3

The body displaces 100m north and then 70m east.
Let Ā (position vector) = 100m due north and Ē(position vector) = 70m due east. Then the displacement is the resultant of the two vectors Ā and Ē.

The angle theta between the two vectors is 90° (refer the position of four cardinal directions i.e.,north , south, east and west.)

Using triangle law of vector addition,
Resultant = Square root (|Ā|² + |Ē|² + 2|Ā||Ē|cos theta )
= Square root ( 100² + 70² + 2(100)(70)cos90°)
● cos 90° = 0
= Square root ( 100² + 70² + 0)
Therefore,
resultant = square root (14900)
= 122.06 or 122.1 m