Determine the bearing on which a car drives from a park if it finishes 30 *2
km east and 75 km south.
Your answer

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Determine the bearing on which a car drives from a park if it finishes 30 *2 km east and 75 km south. Your answer

UpStudy AI · Accepted Answer

1. Let the car’s displacement be represented by its east and south components. The car goes  
   - $$60$$ km east  
   - $$75$$ km south  
   (Here we interpret “30 *2 km east” as $$30 \times 2 = 60$$ km.)

2. The displacement vector is  
   $$
   \vec{D} = \langle 60, -75 \rangle,
   $$
   where east is the positive $$x$$-direction and south is the negative $$y$$-direction.

3. In navigation, bearings are measured clockwise from the north. Since the car travels in the southeast direction, its bearing can be expressed as “South $$\phi$$ East,” where  
   $$
   \phi = \arctan\left(\frac{\text{east component}}{\text{south component}}\right).
   $$
   Using absolute values,
   $$
   \phi = \arctan\left(\frac{60}{75}\right).
   $$

4. Calculating,
   $$
   \phi = \arctan(0.8) \approx 38.66^\circ.
   $$
   This means the car’s direction is $$38.66^\circ$$ east of due south, i.e., S$$38.66^\circ$$E.

5. To convert this into a three-figure bearing (measured clockwise from north), note that due south is $$180^\circ$$ from north. Since the direction is $$38.66^\circ$$ east of south, the bearing is:
   $$
   180^\circ - 38.66^\circ \approx 141.34^\circ.
   $$

6. Thus, the bearing on which the car drives is approximately  
   $$
   141.3^\circ.
   $$
The car's bearing is approximately 141.3 degrees.

Determine the bearing on which a car drives from a park if it finishes 30 *2
km east and 75 km south.
Your answer

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