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A jogger runs 6.0 km [E], then 4.0 km [N], and finally 2.0 km [W]. The entire trip takes 2.0 h to complete. Calculate the jogger's
(a) average speed
(b) average velocity

Sagot :

(a) The trip covers a total distance of 6.0 + 4.0 + 2.0 = 12.0 km, so the jogger's average speed is (12.0 km)/(2.0 h) = 6.0 km/h.

(b) The jogger undergoes a total displacement given by the vector

(6.0 km) i + (4.0 km) j + (-2.0 km) i = (4.0 km) (i + j)

where i is the unit vector pointing due East and j is the unit vector pointing due North. This vector has magnitude

||(4.0 km) (i + j)|| = (4.0 km) √(1² + 1²) ≈ 5.7 km

so the jogger's average velocity is approximately (5.7 km)/(2.0 h) ≈ 2.8 km/h.

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