Answer:
a) The magnitude of your average velocity during the 121 s is 8.61 m/s.
b) The direction of the average velocity is 61.9° south of west.
c) Your average speed during the trip is 11.7 m/s
Explanation:
Hi there!
a) The average velocity (a.v) is calculated as the displacement divided by the time it took to do such a displacement.
The displacement is calculated as the distance between the initial position and the final position:
Displacement = Δ(x,y) = final position - initial position
Let's consider that your initial position is the origin of our frame of reference and let's also consider that west and south are positive directions (+x and +y respectively). Then the displacement vector will be:
Δ(x,y) = final positon - initial position
Δ(x,y) = (490, 920) m - (0, 0) m = (490, 920) m
The 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
The magnitude of the average velocity is calculated as follows:
The magnitude of your average velocity during the 121 s is 8.61 m/s.
b) To find the direction of the average velocity, we have to use trigonometric rules of right triangles. Notice that the x and y-components of the average velocity (vx and vy) together with the average velocity vector (v), with magnitude 8.61 m/s, form a triangle (see figure).
Also, notice that v is the hypotenuse of the triangle and that vx is the side adjacent to the angle θ while vy is the side opposite to θ.
Using trigonometry, we can calculate the value of 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 direction of the average velocity is 61.9° south of west.
c) The average speed (a.s) is calculated as the traveled distance (d) divided by the time it took to cover that distance (t). In total, you traveled (490 m + 920 m) 1410 m in 121 s, then the average speed will be:
a.s = d/t
a.s = 1410 m / 121 s
a.s = 11.7 m/s
Your average speed during the trip is 11.7 m/s
