Galois drove 40kilometers due west in 9hours and then drove 62kilometers due north in 5 hours.
What was his dispacement?
What was his average velocity?
Displacement d =sqrt(s1² + s2)²) =
=sqrt (40² +62²) =73.8 km.
Average velocity
V(ave) = d/t = 73.2/14 =5.3 km/hr.
Note!
Average speed is (40+62)/14 =7.3 km/hr
Awsome thank you. Now I've been trying to figure out how far he traveled but my equation keeps giving me the wrong answer. How would I figure this out?
To find Galois' displacement, we need to determine the straight-line distance and direction from his starting point to his final position. To do that, we can use the Pythagorean theorem to calculate the magnitude of his displacement and trigonometry to determine the direction.
1. Calculating the Magnitude of Displacement:
The distance Galois traveled west is 40 kilometers, and the distance he traveled north is 62 kilometers. We can consider this as a right triangle with two sides:
- The westward distance as the horizontal leg (a) = 40 kilometers
- The northward distance as the vertical leg (b) = 62 kilometers
We can use the Pythagorean theorem to find the hypotenuse (c), which represents Galois' displacement:
c^2 = a^2 + b^2
c^2 = (40^2) + (62^2)
Calculating c:
c^2 = 1600 + 3844
c^2 = 5444
c ≈ √5444
c ≈ 73.8 kilometers
Therefore, Galois' displacement is approximately 73.8 kilometers.
2. Determining the Direction of Displacement:
To find the angle or direction of Galois' displacement, we can use trigonometry, specifically the tangent function. We will calculate the angle formed between the displacement vector and the west direction.
tan(θ) = (b/a)
tan(θ) = 62/40
Calculating θ:
θ = tan^(-1)(62/40)
θ ≈ 56.3 degrees
Therefore, Galois' displacement is approximately 73.8 kilometers at an angle of approximately 56.3 degrees with respect to the west direction.
Now, let's calculate the average velocity.
Average velocity is found by dividing the displacement by the time.
Average velocity (v_avg) = displacement / time
Given Galois drove 40 kilometers west in 9 hours and then 62 kilometers north in 5 hours, we can add the respective time intervals.
Total time taken (t_total) = 9 hours + 5 hours
t_total = 14 hours
Calculating the average velocity:
v_avg = displacement / t_total
v_avg = 73.8 kilometers / 14 hours
v_avg ≈ 5.27 kilometers/hour
Therefore, Galois' average velocity is approximately 5.27 kilometers per hour.