A skater glides along a circular path of radius 7.90 m. If he coasts around one

Question

A skater glides along a circular path of radius 7.90 m. If he coasts around one half of the circle, find the magnitude of the displacement vector (in m) A: 6.16 OB: 7.21OC: 8.43 D: 9.87E: 11.54F: 13.50 G: 15.80H: 18.49 Submit Answer Tries 0/3 What distance has the person skated? n m A: 8.14B: 11.80OC: 17.12D: 24.82 E: 35.99F: 52.18G: 75.66 H: 109.71 Submit Answer Tries 0/3 If the skater coasts only around 73 degrees of the circle, find the magnitude of his displacement vector (in m) A: 3.08OB: 4.47C: 6.48 D: 9.40E: 13.63 F: 19.76 G: 28.65 H: 41.54 Tries 0/3 What distance has he skated in this case? Submit Answer (in m A: 4.12B: 5.15C: 6.44 D: 8.05E: 10.07 F: 12.58 G: 15.73 H: 19.66 Submit Answer Tries 0/3 What is the magnitude of the displacement if he skates all the way around the circle? in m 4 0.00 :0200.3000.02 0.0 1.30 H 1.0 A: 0.00OB: 0.20C: 0.30D: 0.43E: 0.62F: 0.90 G: 1.30 H: 1.89 Submit Answer Tries 0/3

Explanation / Answer

The displacement vector describes a straight line from the starting point to the end point. With a displacement vector, it doesn't matter how you got there.

So, for one half of the circle, displacement is nothing but the diameter.

D = 2r = 2*7.9 = 15.80m

Distance = ½ * circumference = pi*r = pi*7.9 = 24.82m

For 73 degrees:

Distance= (73/360) 2pi*r = (73/360) 2pi*7.9 = 10.3m

Displacement = distance = 10.3m

If he skates all the way around the circle, he ends up right back where he started. Again, the magnitude of displacement really means "How far away did he end up from where he started?" Since he is exactly where he started, his magnitude of displacement is 0 meters.

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