Halliday, Resnick & Walker — Force and Motion–I: Problem 32

Figure 5.22 shows an overhead view of a 0.0250 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force \(\vec{F}_1\) has a magnitude of 6.00 N and is at \(\theta_1 = 30.0^\circ\). Force \(\vec{F}_2\) has a magnitude of 7.00 N and is at \(\theta_2 = 30.0^\circ\). In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity \(\vec{v} = (13.0\hat{i} - 14.0\hat{j})\) m/s, and (c) has the varying velocity \(\vec{v} = (13.0t\hat{i} - 14.0t\hat{j})\) m/s, where \(t\) is time?