Question

Subtracting Vectors Graphically: Example Problem Tallula cycles with a velocity of 5.0" [N]. She then turns a corner and cycles at 5.0" [E]. What is her change in velocity? AŬ = 7.1" [SE] S

Answer 1

1)

5 m/s 5 m/s AV

Consider $\Delta$ V as the change in velocity.
$\Delta$ V = SQRT[v² + v²]
= SQRT[5² + 5²]
= SQRT[50]
= 7.1 m/s
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2)
Consider that north is along y-axis and east is along
Initial displacement, d1 = 5 * cos(38) $\hat{x}$ + 5 * sin(38) $\hat{y}$
Final displacement, d2 = 8 * sin(25) $\hat{x}$ - 8 * cos(25) $\hat{y}$

Total displacement, d = d1 + d2
= [5 * cos(38) + 8 * sin(25)] $\hat{x}$ + [5 * sin(38) - 8 * cos(25)] $\hat{y}$
= 7.32 $\hat{x}$ - 4.17 $\hat{y}$
|d| = SQRT(7.32)² + (-4.17)²]
= SQRT[71]
= 8.43 m