Aditi Chauhan
Last Activity: 9 Years ago
Assumption:
Let us assume that the vector
represents the eastward motion of the car with a magnitude of , the northward motion of the car is given by vector
with a magnitude of 32 km while the east of north motion by vector
with a magnitude of
27 km.
The figure below shows the vector diagram of the Car’s motion:

In vector
, there is no vertical component but only the horizontal component along the east with magnitude 54 km. Therefore vector
is:

For vector
, there is no horizontal component as it describes the northward motion of the car, along the unit vector
.
The magnitude of the vertical component of the car is 32 km, therefore vector
can be written as:

From the vector diagram above, it is clear that the horizontal component of vector
points in the direction of unit vector
. Therefore the horizontal component of vector
is .
27 km sin (28°)
The vertical component of the vector
points northward, along the unit vector
, therefore the component is.27 km cos(28°) .
Therefore vector
is:

The magnitude of total vertical displacement (say sv) of the car along the north is the sum of vertical component of vector
, the vertical component of vector
and the vertical component of vector
.
Since vector
does not have a vertical component, we add the vertical component of vector
and
, to obtain the magnitude of displacement sv as:

The magnitude of total horizontal displacement (say sh) of the car along the east is the sum of horizontal component of vector
, the horizontal component of vector
and the horizontal component of vector
.
Since vector
does not have a horizontal component, we add the horizontal component of vector
and
, to obtain the magnitude of displacement sh as:
…
The magnitude of net displacement (say s) of the car can be calculated using the magnitude in equation (1) and (2) as:

Rounding off to two significant figures
s = 87 km
Therefore the magnitude of displacement of the car during his journey is 87 km .