omvu/O/c MJMZNZQOMJAZMTY4/a/MjcSNzkZNJCWNJcw/details Distance and Displacement Worksheet For each question, plot the path on the grid paper: Fran drives 60km north. Then she drives back 40km south. What distance did she cover? What was her displacement? Nicaria drives her scooter 10 kilometres east. What distance did she cover? She stops for lunch and then drives 5 kilometres. What was her displacement? Ivan walks to the Wendy’s for lunch. He walks 3km east, then 2 km south, and then 10 km east. What distance did he cover? What was his displacement? On his fishing trip, Joshua rides in a boat 15 km south. The fish are biting west. They then follow a school of fish, so they go 6 km north. What distance did they cover? What was their displacement?
The Correct Answer and Explanation is:
Let’s break down the questions and solve them step by step.
- Fran’s Drive:
- Fran first drives 60 km north and then drives 40 km south.
- Distance covered: This is the total length of the path traveled, so it’s 60 km + 40 km = 100 km.
- Displacement: Displacement is the straight-line distance between the starting and ending points, including direction. Fran started 60 km north, and then drove 40 km south, so she ended 20 km north of her starting point. Therefore, her displacement is 20 km north.
- Nicaria’s Scooter Ride:
- Nicaria drives 10 km east, then stops for lunch, and then drives another 5 km.
- Distance covered: Total distance is 10 km + 5 km = 15 km.
- Displacement: Since she only moved east and there is no other change in direction, the displacement is a straight line along her path, which is 15 km east.
- Ivan’s Walk:
- Ivan walks 3 km east, then 2 km south, and then 10 km east.
- Distance covered: This is simply the total length of the path: 3 km + 2 km + 10 km = 15 km.
- Displacement: Ivan’s final position is 13 km east (3 km + 10 km east) and 2 km south. To calculate the displacement, we can use the Pythagorean theorem: Displacement=(132+22)=169+4=173≈13.15 km\text{Displacement} = \sqrt{(13^2 + 2^2)} = \sqrt{169 + 4} = \sqrt{173} \approx 13.15 \, \text{km}Displacement=(132+22)=169+4=173≈13.15km Ivan’s displacement is about 13.15 km in a southeast direction.
- Joshua’s Boat Trip:
- Joshua first rides 15 km south, then 6 km north.
- Distance covered: The total distance traveled is 15 km south + 6 km north = 21 km.
- Displacement: Since Joshua ended 9 km south of his starting point (15 km south minus 6 km north), his displacement is 9 km south.
In summary:
- Fran covered 100 km and her displacement is 20 km north.
- Nicaria covered 15 km and her displacement is 15 km east.
- Ivan covered 15 km and his displacement is about 13.15 km southeast.
- Joshua covered 21 km and his displacement is 9 km south.
