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Carnegie Mellon University

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Problem 35 Medium Difficulty

Towns $A$ and $B$ in Figure $P 3.35$ are 80.0 km apart. A couple arranges to drive from town $A$ and meet a couple driving from town $\mathrm{B}$ at the lake, $\mathrm{L}$ . The two couples leave simultaneously and drive for 2.50 $\mathrm{h}$ in the directions shown. Car 1 has a speed of 90.0 $\mathrm{km} / \mathrm{h}$ . If the cars arrive simultaneously at the lake, what is the speed of car 2 ?

Answer

$v _ { 1 \mathrm { B } } = 68.94 \mathrm { km } \mathrm { h } ^ { - 1 }$

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Video Transcript

so we can first say that a L line segment A l is equaling the sub one times T. This would be equaling 90 0.0 kilometers per hour, multiplied by two and 1/2 hours, 2.50 hours and this is giving us 225 kilometers. Now. We can say that line segment B D or the distance between B D is equaling a D minus a B, and this is essentially equaling a L Co sign of 40 degrees minus 80 kilometers. And so this is giving us 92 0.4 kilometers after subbing in 225 kilometres for a L now from the Triangle B L D. We can say that B l will be equaling the square root of B d quantity squared plus d l quantity squared and this is giving us the square root of 92.4 kilometers quantity squared plus et al sign of 40 degrees quantity squared again. You're substituting 225 kilometres for a L, and we find that B O is equaling 172 kilometers. So now, because car to travels this distance in two and 1/2 hours. We can say that the velocity four Car two is gonna be equaling. 172 kilometers divided by again. Two and 1/2 hours. 2.50 hours. And this is giving us 68.8 kilometers per hour for the constant velocity. Four card too. That is the end of the solution. Thank you for watching.

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