Mark Ladewig posted on Jun 22, 2023 8:02 AM Mr. Ladewig takes his young son for a walk. Together they walk $1000 \mathrm{~m}[\mathrm{~W} 25 \mathrm{~N}]$ in 0.35 hours. They then turn and travel $400 \mathrm{~m}$ [S $35 \mathrm{~W}$ ] in 0.65 hours. Use the COMPONENT METHOD to determine the average velocity of the entire walk. Exam Review Change

Step 1 ：Find the components of each displacement: For the first displacement, \(1000\mathrm{~m} [\mathrm{~W} 25\mathrm{~N}]\), we have \(x_1 = -1000\cos{25^\circ}\) and \(y_1 = 1000\sin{25^\circ}\). For the second displacement, \(400\mathrm{~m} [\mathrm{S} 35\mathrm{~W}]\), we have \(x_2 = -400\cos{35^\circ}\) and \(y_2 = -400\sin{35^\circ}\).

Step 2 ：Calculate the components: \(x_1 = -1000\cos{25^\circ} \approx -906.31\mathrm{~m}\), \(y_1 = 1000\sin{25^\circ} \approx 422.62\mathrm{~m}\), \(x_2 = -400\cos{35^\circ} \approx -327.57\mathrm{~m}\), and \(y_2 = -400\sin{35^\circ} \approx -229.76\mathrm{~m}\).

Step 3 ：Find the total displacement components: \(x = x_1 + x_2 \approx -906.31\mathrm{~m} - 327.57\mathrm{~m} = -1233.88\mathrm{~m}\) and \(y = y_1 + y_2 \approx 422.62\mathrm{~m} - 229.76\mathrm{~m} = 192.86\mathrm{~m}\).

Step 4 ：Calculate the magnitude of the total displacement: \(d = \sqrt{x^2 + y^2} = \sqrt{(-1233.88\mathrm{~m})^2 + (192.86\mathrm{~m})^2} \approx 1251.47\mathrm{~m}\).

Step 5 ：Find the total time: \(t = 0.35\mathrm{~hr} + 0.65\mathrm{~hr} = 1\mathrm{~hr}\).

Step 6 ：Calculate the average velocity: \(v = \dfrac{d}{t} = \dfrac{1251.47\mathrm{~m}}{1\mathrm{~hr}} = 1251.47\mathrm{~m/hr}\).

Step 7 ：\(\boxed{1251.47}\mathrm{~m/hr}\) is the average velocity of the entire walk.