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The diagram below shows the velocities of two cyclists. 7 mathrm(~m) / mathrm(s) west Cycilist 1 4 mathrm(~m) / mathrm(s) west Cyclist 2 From the frame of reference of cyclist 1, what is the velocity of cyclist 2? A. 4 mathrm(~m) / mathrm(s) east B. 4 mathrm(~m) / mathrm(s) west C. 3 mathrm(~m) / mathrm(s) west D. 3 mathrm(~m) / mathrm(s) east

Question

The diagram below shows the velocities of two cyclists.
 7 mathrm(~m) / mathrm(s) west
Cycilist 1
 4 mathrm(~m) / mathrm(s) west
Cyclist 2
From the frame of reference of cyclist 1, what is the velocity of cyclist 2?
A. 4 mathrm(~m) / mathrm(s) east
B. 4 mathrm(~m) / mathrm(s) west
C. 3 mathrm(~m) / mathrm(s) west
D. 3 mathrm(~m) / mathrm(s) east

The diagram below shows the velocities of two cyclists. 7 mathrm(~m) / mathrm(s) west Cycilist 1 4 mathrm(~m) / mathrm(s) west Cyclist 2 From the frame of reference of cyclist 1, what is the velocity of cyclist 2? A. 4 mathrm(~m) / mathrm(s) east B. 4 mathrm(~m) / mathrm(s) west C. 3 mathrm(~m) / mathrm(s) west D. 3 mathrm(~m) / mathrm(s) east

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EfaExpert · Tutor for 3 years

Answer

### D. \( 3 \mathrm{~m} / \mathrm{s} \) east

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## Step 1: Identify the frame of reference<br />### From cyclist 1's perspective, treat cyclist 1's velocity as zero.<br />## Step 2: Calculate relative velocity of cyclist 2<br />### Subtract the velocity of cyclist 1 from the velocity of cyclist 2 to determine the relative velocity.<br />\[<br />\text{Relative Velocity} = v_{\text{cyclist 2}} - v_{\text{cyclist 1}}<br />\]<br />\[<br />\text{Relative Velocity} = 4 \mathrm{~m/s} \, \text{west} - 7 \mathrm{~m/s} \, \text{west}<br />\]<br />\[<br />\text{Relative Velocity} = -3 \mathrm{~m/s} \, \text{west}<br />\]<br />### The negative sign indicates the opposite direction, so \(3 \, \text{m/s}\) east.
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