Question

A car is driven from Bhubaneswar to New Delhi and the difference between the final reading and the initial reading of the odometer is 1850 km. How would one find the displacement of magnitude?

Answer 1

Explanation:

I think it’s impossible to do unless you practically drove in a straight line, straight from Bhubaneswar to New Delhi, with a compass on your car.

Not sure what you meant by “displacement of magnitude” (maybe you mean magnitude of displacement), but you can’t know displacement from simply reading the odometer.

First you have to know the difference between distance and displacement. Distance is the total distance traveled, while Displacement is the distance you “displaced” (I.e. straight line distance between start and finish)

For example, I ran a lap on a 400m track. My distance is 400m, but my displacement is 0m, since I ended up where I started.

So, you may have a distance of 1850km, but I’m sure your displacement is less than that, since you have to turn and don’t travel in a straight line.

Also, displacement is a vector, meaning it must have a direction associated with it, like N30E or S60W.

So how do you find your displacement in this journey?

find a map

Connect your starting point and destination

Measure said distance and scale it back up to real-world size (read the scale, e.g. a scale of 1:20000 mean 1 cm on the map = 20000cm/200m in real life)

Locate direction with a protractor (placed on the starting point)

Join them together and viola! There’s your displacement (should be something like 500km (N45W))

Answer 2

Answer:

Total displacement between Bhubneshwar to Delhi is 1308.32 km.

Explanation:

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

Suppose,

Approximately Distance of X from Bhubaneshwar (from map) $= x km$

                                                                                                       $= 90km$

Approximately Distance of X from Delhi (from map) $=y km$

                                                                                     $=940km$

As per the formula,

$(x+y)^{2} = x^{2} +y^{2} +2xy$

By Pythagoras Theorem:

$x^{2} +y^{2} =z^{2} = (displacement)^{2}$

Hence,

$(x+y)^{2} = z^{2} +2xy$

Then,

$(Displacement)^{2} =(x+y)^{2} -2xy$

$(Displacement)^{2} =(1850)^{2} -2*910*940$

$(Displacement)^{2} =3422500-2*855400$

$(Displacement)^{2} =3422500-1710800$

$(Displacement)^{2} =1711700$

$Displacement =1308.32km$

Total displacement between Bhubneshwar to Delhi is $1308.32 km.$