sph3u1 - unit 1 kinematics\n15. a happy dog is chasing after birds in the park. the dog undergoes the…

sph3u1 - unit 1 kinematics\n15. a happy dog is chasing after birds in the park. the dog undergoes the following motions:\ni. 21 m e 25° s\nii. 36 m w 42° s\na) draw two separate diagrams that represent the x and y - components of the motions above. 2 marks - a\nmotion i\nmotion ii\nb) determine the net displacement of the dog. you may use the component method or sine/cosine law method. be sure to include a diagram representing the net displacement. 6 marks - a

sph3u1 - unit 1 kinematics\n15. a happy dog is chasing after birds in the park. the dog undergoes the following motions:\ni. 21 m e 25° s\nii. 36 m w 42° s\na) draw two separate diagrams that represent the x and y - components of the motions above. 2 marks - a\nmotion i\nmotion ii\nb) determine the net displacement of the dog. you may use the component method or sine/cosine law method. be sure to include a diagram representing the net displacement. 6 marks - a

Answer

Explanation:

Step1: Find x - components of each motion

For motion i: $d_{i,x}=21\cos(25^{\circ})\approx19.03$ m (east - positive x - direction). For motion ii: $d_{ii,x}=- 36\cos(42^{\circ})\approx - 26.76$ m (west - negative x - direction).

Step2: Find y - components of each motion

For motion i: $d_{i,y}=-21\sin(25^{\circ})\approx - 8.87$ m (south - negative y - direction). For motion ii: $d_{ii,y}=-36\sin(42^{\circ})\approx - 24.06$ m (south - negative y - direction).

Step3: Calculate net x - component

$D_x=d_{i,x}+d_{ii,x}=19.03 - 26.76=-7.73$ m.

Step4: Calculate net y - component

$D_y=d_{i,y}+d_{ii,y}=-8.87-24.06=-32.93$ m.

Step5: Calculate net displacement magnitude

$D = \sqrt{D_x^{2}+D_y^{2}}=\sqrt{(-7.73)^{2}+(-32.93)^{2}}\approx33.82$ m.

Step6: Calculate direction

$\theta=\tan^{-1}\left(\frac{D_y}{D_x}\right)=\tan^{-1}\left(\frac{-32.93}{-7.73}\right)\approx76.7^{\circ}$ south of west.

Answer:

The net displacement of the dog is approximately $33.82$ m in the direction of $76.7^{\circ}$ south of west.

(Note: For part (a), for motion i: Draw a vector with magnitude 21 m at an angle of $25^{\circ}$ south of east. Then break it into an x - component (east - direction) and a y - component (south - direction). For motion ii: Draw a vector with magnitude 36 m at an angle of $42^{\circ}$ south of west and break it into x (west - direction) and y (south - direction) components. Diagrams are best drawn on graph paper with appropriate scale and labeled axes.)