Mary walked north from her home to Sheila's home, which is 4.0 kilometers away. Then she turned right and walked another 3.0 kilometers to the supermarket, which is 5.0 kilometers from her own home. She walked the total distance in 1.5 hours. What were her average speed and average velocity?
1. Speed = d/t = (4+3) / 1.5=4.66 km/h.
2. tanA = 4/3 = 1.333,
A = 53.12 Deg.
D = X/cosA = 3/cos53.12 = 5 km @ 53.12 Deg.
V = 5 / 1.5 = 3.33 km/h @ 53 Deg.
To find Mary's average speed and average velocity, we first need to calculate the total distance she traveled and the total displacement.
1. Total Distance:
Mary walked 4.0 kilometers from her home to Sheila's home, then turned right and walked another 3.0 kilometers to the supermarket. Therefore, the total distance she traveled is 4.0 kilometers + 3.0 kilometers = 7.0 kilometers.
2. Total Displacement:
Displacement is the straight-line distance from an initial point to a final point. In this case, Mary's initial point is her home, and her final point is the supermarket. We can use the Pythagorean theorem to calculate the displacement. The displacement can be calculated as follows:
Displacement = √((4.0 km)^2 + (3.0 km)^2) ≈ √(16.0 + 9.0) ≈ √25.0 ≈ 5.0 km
3. Average Speed:
Average speed is calculated by dividing the total distance traveled by the total time taken. In this case, Mary walked a total distance of 7.0 kilometers in 1.5 hours.
Average Speed = Total Distance / Total Time = 7.0 km / 1.5 h ≈ 4.67 km/h
Therefore, Mary's average speed is approximately 4.67 kilometers per hour.
4. Average Velocity:
Average velocity takes both the displacement and the total time into account. It is the ratio of the displacement vector to the total time taken. In this case, Mary's displacement was 5.0 kilometers, and she took 1.5 hours.
Average Velocity = Displacement / Total Time = 5.0 km / 1.5 h ≈ 3.33 km/h
Therefore, Mary's average velocity is approximately 3.33 kilometers per hour.