A cat moving in a desert walks 15m due north, then 6m due east then south calculate the resultant of the cat.
I can not because I do not know how far south the cat walked
To calculate the resultant of the cat's movement, we need to determine both the direction and magnitude of the displacement.
First, let's visualize the cat's movements step by step:
1. The cat walks 15m due north.
2. Then, the cat walks 6m due east.
To find the resultant displacement, we need to find the total north and east components separately and then combine them.
Using the given information:
- The cat starts by moving 15m due north, so we have 15m in the north direction.
- Next, the cat moves 6m due east.
To combine these movements, we use vector addition. We add up the north component with the east component.
The north component remains unchanged at 15m.
For the east component, we can visualize it as a horizontal movement which is perpendicular to the north component. In this case, we can use the Pythagorean theorem to find the length of the resultant displacement. The north and east components form a right-angled triangle.
Using the Pythagorean theorem,
resultant = √(north^2 + east^2)
= √(15^2 + 6^2)
= √(225 + 36)
= √261
Hence, the magnitude of the resultant displacement is √261 units.
Now, to find the direction of the resultant, we can use trigonometry.
Let's define the angle α as the angle between the resultant displacement and north.
Using the tangent function,
tan(α) = east component / north component
tan(α) = 6 / 15
α = arctan(6 / 15)
Evaluating this using a scientific calculator, we find α ≈ 21.801 degrees.
Therefore, the resultant of the cat's movement is approximately √261 units in a direction approximately 21.801 degrees east of north.