Example Question - circular motion
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Running Around a Circular Well
<p>Let the number of complete laps Laura completes before Tom catches up be \( L \).</p> <p>Since Tom completes 10 laps while Laura completes 8 laps, the ratio of their speeds is \( \frac{10}{8} = \frac{5}{4} \).</p> <p>If we set the time taken for Laura to complete \( L \) laps as \( t \), then Tom completes \( \frac{5}{4}L \) laps in the same time, meaning:</p> <p>1 lap for Tom when Laura completes \( \frac{4}{5} \) laps.</p> <p>Thus, when they run together, for every 10 laps of Tom, Laura runs 8 laps. Therefore, to find the total laps before Tom catches her:</p> <p>Set the equation \( 10x = 8(x + 1) \):</p> <p>\( 10x = 8x + 8 \)</p> <p>\( 2x = 8 \)</p> <p>\( x = 4 \)</p> <p>Hence, Laura completes 4 laps before Tom catches her. The answer is:</p> <p>4 complete laps.</p>
Motion Around a Circular Track
<p>Let the circular track be of circumference C. Tom completes 10 rounds, which means he covers a distance of 10C.</p> <p>Laura completes 8 rounds, which means she covers a distance of 8C.</p> <p>The speeds of Tom and Laura can be represented as:</p> <p>Speed of Tom = 10C/t</p> <p>Speed of Laura = 8C/t</p> <p>In order to find how many complete rounds Laura makes before Tom reaches her, we can set up the equation:</p> <p>Speed of Tom = Speed of Laura + distance covered by Laura in time t.</p> <p>Let x be the number of complete rounds Laura runs before Tom catches up with her, which can be expressed as:</p> <p>10C/t = 8C/t + (xC/t).</p> <p>Solving for x:</p> <p>10 = 8 + x,</p> <p>x = 2.</p> <p>Thus, Laura will have completed 2 complete rounds before Tom reaches her for the first time.</p>
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