The footballer walked 40 m across the football field to the north, then 10 m to the east, then 10 m to the south

The footballer walked 40 m across the football field to the north, then 10 m to the east, then 10 m to the south, then 30 m to the east. Find the complete movement module for a football player.

Given:

S1 = 40 meters – the distance traveled by the footballer to the north;

S2 = 10 meters – the distance traveled by the footballer to the east;

S3 = 10 meters – the distance traveled by the footballer to the south;

S4 = 30 meters – the distance traveled by the footballer to the east.

It is required to determine the modulus of the complete movement of a football player S (meter).

Let’s introduce a coordinate system, the OX axis of which will be directed from south to north, and the OY axis – from west to east.

Then the player’s movement along the OX axis will be equal to:

Sx = S1 – S3 = 40 – 10 = 30 meters.

The player’s movement along the OU axis will be equal to:

Sy = S2 + S4 = 10 + 30 = 40 meters.

The total movement will be equal to:

S = (Sx ^ 2 + Sy ^ 2) ^ 0.5 = (30 ^ 2 + 40 ^ 2) ^ 0.5 =

= (900 + 1600) ^ 0.5 = 2500 ^ 0.5 = 50 meters.

Answer: the total movement of a football player is 50 meters.