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?

Question

UpStudy AI · Accepted Answer

**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.

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?

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Geometry Questions