Final answer:
To find the component of vector A along vector B, calculate A's x and y component using A's magnitude and the cosine and sine of its angle. If A and B are perpendicular, A's component along B is zero since cosine of 90° is zero. Then combine the respective x and y components to get the resultant.
Step-by-step explanation:
To find the component of vector A along vector B, you must first calculate the x and y components of each vector. Using the provided magnitudes and angles, for vector A with magnitude 53.0 m and angle 20.0°, the x-component (Ax) is found using the cosine function:
Ax = A cos θ,
where A is the magnitude of vector A, and θ is the angle it makes with the x-axis. Similarly, vector B's x-component (Bx) is found using its magnitude 34.0 m and angle 63.0°. If vectors A and B are perpendicular, the component of A along B would be zero, since the cosine of 90° is zero.
To combine these components, you add the x-components and y-components together separately to find the respective components of the resultant vector along each axis:
Rx = Ax + Bx
Thus, by resolving each vector into its x-axis and y-axis components, you can find the component of one vector along the direction of the other. This principle is used to finally determine the combined effect when the directions of the two vectors are taken into account.