Tammy leaves the office, drives 21 Km due north, then turns onto a second highway and continues in a direction of 31 degree north of east for 87 Km.
What is her total displacement from the office? Answer in units of Km.
D=21N+87cos31N + 87sin31E
figure that out.
At what angle is her displacement? consider east to be 0 degree and north 90 degree
Answer in units of degree
To solve this problem, we can break down Tammy's displacement into horizontal (east-west) and vertical (north-south) components.
1. First, let's calculate the horizontal displacement:
Tammy initially drives 21 Km due north, so her horizontal displacement in this part is 0 Km (since she only moves vertically in this direction).
2. Next, let's calculate the vertical displacement:
Tammy then turns onto the second highway and drives 87 Km in a direction 31 degrees north of east. To find the vertical displacement, we need to find the vertical component of this distance traveled.
To find the vertical component, we can use the equation:
Vertical component = Distance traveled * sin(angle)
Vertical component = 87 Km * sin(31 degrees) = 87 Km * 0.515 = 44.805 Km (rounded to three decimal places)
3. Finally, let's calculate the total displacement using the horizontal and vertical components:
Total displacement = √(Horizontal displacement^2 + Vertical displacement^2)
Total displacement = √(0 Km^2 + 44.805 Km^2) = √(0 + 2005.042) = √2005.042 = 44.769 Km (rounded to three decimal places)
Therefore, Tammy's total displacement from the office is approximately 44.769 Km.
To find Tammy's total displacement from the office, we need to combine her northward and eastward movements using vector addition.
Her northward displacement is 21 km due north, and we can represent this as a vector with magnitude 21 km in the positive y-direction.
Next, her eastward displacement is 87 km in a direction of 31 degrees north of east. To represent this vector, we can break it down into its x and y components. The x-component will be 87 km multiplied by the cosine of 31 degrees, and the y-component will be 87 km multiplied by the sine of 31 degrees.
Now, let's find the x and y components:
x-component: 87 km * cos(31 degrees)
y-component: 87 km * sin(31 degrees)
We can use the following trigonometric identities to find the values:
cos(31 degrees) ≈ 0.8572
sin(31 degrees) ≈ 0.5144
x-component: 87 km * 0.8572
y-component: 87 km * 0.5144
Now, we can calculate the x and y components:
x-component ≈ 74.5904 km
y-component ≈ 44.7952 km
Finally, we can find the total displacement by adding the x and y components. We can use the Pythagorean theorem to calculate the magnitude of the total displacement vector:
Total displacement = √(x-component^2 + y-component^2)
Total displacement ≈ √(74.5904^2 + 44.7952^2) ≈ √(5563.6244 + 2008.0634) ≈ √(7571.6878) ≈ 87.01 km
Therefore, Tammy's total displacement from the office is approximately 87.01 km.