Two particles A and B start at O and travel in opposite direction along the circular path at constant speed V_a = 0.7m/s and V_b = 1.5m/s respectively. Determine the time when they collide(radius = 5m)?

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Explanation:

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Feb 9, 2018

They collide after about 10 s.

Explanation:

The circumference of the circle is $2 \cdot \pi \cdot r = 31.42 m$. Let the distance traveled by them be ${d}_{A} \mathmr{and} {d}_{B}$ respectively. So we know that

${d}_{A} + {d}_{B} = 31.42 m$

Let the time between start and collision be t. Then we know that

${d}_{A} = 0.7 \frac{m}{s} \cdot t \mathmr{and} {d}_{B} = 1.5 \frac{m}{s} \cdot t$

Substituting into the first equation

$0.7 \frac{m}{s} \cdot t + 1.5 \frac{m}{s} \cdot t = 31.42 m$

$t = \frac{31.42 m}{0.7 \frac{m}{s} + 1.5 \frac{m}{s}}$

$t = \frac{31.42 \cancel{m}}{2.2 \frac{\cancel{m}}{s}} = 14.28 s$

So, rounding that to 1 significant digit (because radius is 5 m), they collide after about 10 s.

I hope this helps,
Steve

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