Question

3. To go from your house to a nearby hospital, you must walk 11 m E and then turn 13 m 63º S of W. What is your displacement? Use graphical (parallelogram method) and trigonometric method. (5 points each for graphical and analytical method)

 

4. Make a worded problem with complete solution applying the component method. Use the direction in your house (Starting point: door – going to living room – going to your bed room – going to kitchen – going to CR). Minimum of 4 vectors. (10 points: 3 points – worded Problem; 5 points – correct solution; 2 points – correct answer)

Answer 1

(3) The displacement, according to the sketch below, is 12 m.

Find displacement analytically:

$$R_E=A\cos\theta_A-B\cos\theta_B=\\=11\cos0-13\cos63°=5.1\text{ m}.\\ R_S=A\sin\theta_A+B\sin\theta_B=\\=11\sin0+13\sin63°=11.6\text{ m}.\\ R=\sqrt{R_E^2+R_S^2}=12.7\text{ m}.$$

(4) In my house, the vectors are as follows:

A: door – going to living room: 5 m N

B: living room - going to bed room: 4 m W

C: bed room – going to kitchen: 5 m N

D: kitchen – going to CR: 4 m W

Find displacement using component method:

$$R_N=A_N+C_N=5+5=10\text{ m},\\ R_W=B_W+D_W=4+4=8\text{ m},\\ R=\sqrt{R_N^2+R_W^2}=12.8\text{ m}.$$