An ant walks 22.0cm in a northernly direction, turns and walks southeasterly (45° east of south) a distance of 47.0cm what is the resultant displacement?
To find the resultant displacement, we can break down the ant's movements into its north-south and east-west components.
First, let's calculate the north-south component. The ant walks 22.0 cm in a northernly direction, so this distance is the ant's north-south displacement.
Secondly, let's calculate the east-west component. The ant walks in a southeasterly direction, which means it's moving both south and east. Since the ant is moving 45° east of south, we can use trigonometry to find the east-west component. We can use the formula:
east-west component = distance * cos(angle)
Using the values given, the distance is 47.0 cm and the angle is 45°. So the east-west component is:
east-west component = 47.0 cm * cos(45°)
Using the trigonometric relationship: cos(45°) = √2 / 2, we can simplify the equation:
east-west component = 47.0 cm * (√2 / 2)
east-west component = 33.24 cm
Now we have the north-south component (22.0 cm) and the east-west component (33.24 cm). To find the resultant displacement, we can use the Pythagorean theorem:
resultant displacement = √(north-south component^2 + east-west component^2)
resultant displacement = √(22.0 cm^2 + 33.24 cm^2)
resultant displacement ≈ √(484 cm^2 + 1104.4576 cm^2)
resultant displacement ≈ √(1588.4576 cm^2)
resultant displacement ≈ 39.86 cm
Therefore, the resultant displacement of the ant is approximately 39.86 cm.