problem 1.4 - resolve the 120 - n force into components acting in the given u and v directions.

Explanation:

Step1: Find angle between force and u - direction

The angle between the 120 - N force and the u - direction is $\theta_{u}=40^{\circ}$.

Step2: Calculate component in u - direction

Using the formula $F_{u}=F\cos\theta_{u}$, where $F = 120$ N and $\theta_{u}=40^{\circ}$, we have $F_{u}=120\cos40^{\circ}\approx120\times0.766 = 91.92$ N.

Step3: Find angle between force and v - direction

The angle between the 120 - N force and the v - direction is $\theta_{v}=25^{\circ}$.

Step4: Calculate component in v - direction

Using the formula $F_{v}=F\cos\theta_{v}$, where $F = 120$ N and $\theta_{v}=25^{\circ}$, we have $F_{v}=120\cos25^{\circ}\approx120\times0.9063 = 108.756$ N.

Answer:

The component of the 120 - N force in the u - direction is approximately 91.92 N and in the v - direction is approximately 108.76 N.