Answer:
a) Your average velocity's magnitude over the course of 121 seconds is 8.61 m/s.
b) The average velocity's direction is at an angle of 61.9° south from west.
c) During this journey, your average speed calculates to be 11.7 m/s.
Explanation:
Hello!
a) Average velocity (a.v) is determined by dividing the total displacement by the time taken to achieve it.
Displacement is the difference between the starting and ending positions:
Displacement = Δ(x,y) = final position - initial position
If we assume the starting location is the origin of our reference frame with west and south as positive directions (+x and +y, respectively), the displacement vector can be represented as:
Δ(x,y) = final position - initial position
Δ(x,y) = (490, 920) m - (0, 0) m = (490, 920) m
The calculation for average velocity will be:
a.v = Δ(x,y) / t
a.v = (490, 920) m / 121 s
a.v = (4.05, 7.60) m/s
To find the magnitude of the average velocity:
The magnitude of your average velocity over the 121 seconds is 8.61 m/s.
b) To find the average velocity's direction, trigonometric principles involving right triangles are necessary. Notice that the x and y components of average velocity (vx and vy), along with the average velocity vector (v, magnitude 8.61 m/s), create a triangle (refer to the figure).
Notice that v acts as the triangle's hypotenuse, vx is the adjacent side to the angle θ, and vy is the opposite side to θ.
Using trigonometric identities, we can derive the angle θ:
cos θ = adjacent side / hypotenuse
cos θ = vx / v
cos θ = 4.05 m/s / 8.61 m/s
θ = 61.9°
The average velocity points at 61.9° south of west.
c) The average speed (a.s) is determined by the total distance (d) traveled divided by the duration (t) it took to traverse that distance. You covered a total distance of (490 m + 920 m) which equals 1410 m in 121 seconds. Therefore, the average speed computation is:
a.s = d/t
a.s = 1410 m / 121 s
a.s = 11.7 m/s
Your average speed for the trip is 11.7 m/s
