Question

A car is going from Bhubaneshwar to New Delhi. The difference between the initial and final readings of odometer is 1850 km. Find the magnitude of total displacement between Bhubaneshwar and New Delhi using the road map of India.

Answer 1

Let point X along longitude of Delhi and Latitude of Bhubaneshwar. Then

Suppose,
Approximately Distance of X from Bhubaneshwar (from map) = x = 910 km
Approximately Distance of X from Delhi (from map) = y = 940 km

as per the formula;
(x + y)2 = x2 + y2 + 2xy

By pythagoras theorem:
x2 + y2 = z2 = (displacement)2
Hence,
(x + y)2 = z2  + 2xy
Then,
(Displacement)2 = (x + y)2 -  2xy
(displacement)2 = (1850)2 - 2(910 x 940)
(displacement)2 = 3422500 - 2 x 855400
(displacement)2 = 3422500 - 1710800
(displacement)2 = 1711700
displacement = 1308.32 km

Total displacement between Bhubneshwar to Delhi is 1308.32 km


hope it helps you!!