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Dog runs: 25.0m [E23°N], 30.0m [S37°W], 45.0m [W67°N] They take 75s for the entire trip. What was the average velocity of the dog?
Find Total Displacement, then divide that by time
A.
Conventions
25m
23°
x_A = 25 cos(23) = 23.0126 y_A = 25 sin(23) = 9.7682
30m
37°
x_B = -(30 sin37) = -18.0545 y_B = -(30 cos37) = -23.9591
B.
67°
45m
x_C = -(45 cos(67)) = -17.5829 y_C = 45 sin(67) = 41.4227
C.
Δd_x = 23.0126 - 18.0545 - 17.5829 = -12.6248
Total displacement vector:
12.6248
27.2318
sqrt((-12.6248)^2 + (27.2318)^2) = 30.0159m
Δd_y = 9.7682 - 23.9591 + 41.4227 = 27.2318
arctan( 27.2318 / 12.6248 ) = 65°
65°
30.0159m
v = d/t it will retain the same angle
Total velocity vector:
v = 30.0159/75 = 0.4
v_avg = 0.4m/s[W65°N]