If he travels 7.0 km 40 degree west of north then 10.0 km east, find the resultant displacement
To find the resultant displacement, we can use vector addition.
Step 1: Draw a rough diagram of the given information.
First, draw the initial displacement of 7.0 km in the direction 40 degrees west of north. This can be represented as an arrow pointing upward at an angle of 40 degrees.
Next, draw the second displacement of 10.0 km directly east. This can be represented as an arrow pointing to the right.
Step 2: Break down the vectors into their x-component and y-component.
The initial displacement of 7.0 km west of north can be broken down into two components: the x-component (horizontal) and the y-component (vertical).
The x-component can be calculated by using the cosine of the angle:
x-component = 7.0 km * cos(40 degrees)
The y-component can be calculated by using the sine of the angle:
y-component = 7.0 km * sin(40 degrees)
Since the second displacement is directly east, its x-component is 10.0 km and its y-component is 0.
Step 3: Add the x-components and the y-components separately.
Add the x-components together:
x-component resultant = x-component initial + x-component second
Add the y-components together:
y-component resultant = y-component initial + y-component second
Step 4: Calculate the magnitude and direction of the resultant displacement.
Use the Pythagorean theorem to calculate the magnitude of the resultant displacement:
magnitude resultant = square root((x-component resultant)^2 + (y-component resultant)^2)
To find the direction of the resultant displacement, use the inverse tangent function:
direction resultant = arctan(y-component resultant / x-component resultant)
Step 5: Substitute the calculated values to find the final answer.
Now, calculate the x-component and y-component for the initial displacement:
x-component initial = 7.0 km * cos(40 degrees)
y-component initial = 7.0 km * sin(40 degrees)
The x-component and y-component for the second displacement are:
x-component second = 10.0 km
y-component second = 0
Adding the x-components and y-components:
x-component resultant = x-component initial + x-component second
y-component resultant = y-component initial + y-component second
Calculating the magnitude and direction of the resultant displacement:
magnitude resultant = square root((x-component resultant)^2 + (y-component resultant)^2)
direction resultant = arctan(y-component resultant / x-component resultant)
Finally, substitute the calculated values to find the resultant displacement.