2. A bike went $$ 150 \mathrm{~m} \mathrm{E}, 40 \mathrm{~m} \mathrm{~N}, 100 \mathrm{~m} \mathrm{~W} $$, and 40 m S. a. What is the bike's resultant displacement? b. What should be the bike's next displacement to get back to the starting point?

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**a. Calculate the resultant displacement**

1. Break each displacement into horizontal (east-west) and vertical (north-south) components:
   - $$150\,\mathrm{m}$$ East: horizontal $$+150$$ m.
   - $$40\,\mathrm{m}$$ North: vertical $$+40$$ m.
   - $$100\,\mathrm{m}$$ West: horizontal $$-100$$ m.
   - $$40\,\mathrm{m}$$ South: vertical $$-40$$ m.

2. Sum the horizontal components:
   $$
   150 - 100 = 50\,\mathrm{m} \quad (\text{East})
   $$

3. Sum the vertical components:
   $$
   40 - 40 = 0\,\mathrm{m}
   $$

4. The resultant displacement is:
   $$
   50\,\mathrm{m}\, \text{East}
   $$

**b. Determine the displacement to return to the starting point**

1. Since the bike's current displacement is $$50\,\mathrm{m}$$ East, the displacement required to return to the starting point must cancel this out.

2. Therefore, the bike must travel:
   $$
   50\,\mathrm{m}\, \text{West}
   $$
**a. Resultant Displacement:** - The bike is $$50\,\mathrm{m}$$ East of the starting point. **b. Next Displacement to Return:** - The bike should travel $$50\,\mathrm{m}$$ West to return to the starting point.

A bike went , and 40 m S.
a. What is the bike’s resultant displacement?
b. What should be the bike’s next displacement to get back to the starting point?

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A bike went , and 40 m S. a. What is the bike’s resultant displacement? b. What should be the bike’s next displacement to get back to the starting point?