Final answer:
To find the magnitude and direction of f2 for a resultant upward force on the z-axis, cancel out the horizontal components and use vector addition and trigonometry for the vertical z-component, combined with existing forces to achieve a total force of 275 N.
Step-by-step explanation:
To determine the magnitude and direction angles of f2 so that the resultant of the two forces acts upward along the z-axis and has a magnitude of 275 N, we can use vector addition and trigonometry. First, we need to ascertain that the force exerted by f2 is such that when combined with the existing forces, the outcome aligns vertically upwards. Given that we want a resultant force along the z-axis only, we need to ensure that the force components in the x and y directions from all forces cancel out.
To achieve the required vertical effect, we need to find the missing z-component of f2 that will produce a total upward force of 275 N when vectorially added to the z-components of other forces. We disregard the x and y components for this calculation since the outcome must only focus on the z-direction. Once we have the z-component, we apply the Pythagorean theorem and trigonometric functions to find the magnitude and direction angles.