[2025-26] SPH3U Phys ...

Follow the Problem Set Instructions & Rubric to complete and submit the following questions:

1. Determine the components of the vector \(2.50 m [N 38.0^o W]\). 

2. A student walks \(25.0m [E 30.0^o N]\). Determine the components of the student's displacement.

3. A vector has the following components: \( \Delta d_x = 54 m [E]\) and \( \Delta d_y = 24 m [N]\).
a) Calculate the length of the total displacement vector.
b) Determine the vector's direction. 

4. A driver travels \(15.0 km\) to the west and then turns and drives \(45.0 km\) to the south. Finally, she travels \( 32 km [N 25^o W]\). Determine the driver's total displacement. 

5. Using components, determine the total displacement from the following individual displacements: \( \Delta \vec{d}_1 = 2.5 m [W 30.0^o S], \Delta \vec{d}_2 = 3.6 m [S]\), and \( \Delta \vec{d}_3 = 4.9 m [E 38.0^o S]\).

6. A boat travelling on the St. Lawrence River moves \( 2.70 km [E 25.0^o N] and then changes direction and moves \(4.80 km [E 45.0^o S]\). Determine 
a) the components of the total displacement
b) the total displacement of the boat

ANSWERS:
1. \( \Delta \vec{d}_x = 1.54m [W]\); \( \Delta \vec{d}_y = 1.97m [N]\)
2. \( \Delta \vec{d}_x = 21.7m [E]\); \( \Delta \vec{d}_y = 12.5m [N]\)
3. \(59m [E24^oN]\)
4. \(32.7 km [W29^oS]\)
5. \(8.1m [S 12^o E]\)
6. a) \( \Delta \vec{d}_x = 5.84km [E]\); \( \Delta \vec{d}_y = 2.25km [S]\); b) \(6.26km [E21^oS]\)