Anne flies due east from san Francisco to Washington dc a displacement of 5600 km. She then flies from Washington to Boston a displacement of 900 km at an angle of 55 degrees east of north. What is Anne's total displacement?
To find Anne's total displacement, we need to combine the displacements from her flight from San Francisco to Washington, D.C. and from Washington, D.C. to Boston.
The displacement from San Francisco to Washington, D.C. is given as 5600 km due east. This means that the direction of travel is directly east without any deviation. So, the displacement is purely in the x-axis direction.
The displacement from Washington, D.C. to Boston is given as 900 km at an angle of 55 degrees east of north. Let's break this down into its x and y components.
The x-component of the displacement is the magnitude of the displacement multiplied by the cosine of the angle. So, the x-component is:
x = 900 km * cos(55°)
Similarly, the y-component of the displacement is the magnitude of the displacement multiplied by the sine of the angle. So, the y-component is:
y = 900 km * sin(55°)
Now, we can combine the x-components and y-components of the displacements to find the total displacement. Since the displacement from San Francisco to Washington is purely in the x-axis direction, the y-component is zero. So, the total displacement is:
Total displacement = 5600 km (in the x-axis direction) + x (x-component from Washington to Boston) + y (y-component from Washington to Boston)
Total displacement = 5600 km + x + y
Now, you can calculate the x and y components using the given angle, and then substitute those values into the equation above.