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quiz_04C - t so each equation has two solutions t = 1 t = 3...

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Math 213 — Quiz 4 Name Solution 1. Suppose that two particles travel along the paths r 1 ( t ) = h t 2 , 7 t - 12 , t 2 i , r 2 ( t ) = h 4 t - 3 , t 2 , 5 t - 6 i , for t 0. Do the particles collide? If so, say exactly where and when they do. The particles will collide at time t if r 1 ( t ) = r 2 ( t ). From this vector equation, we get three coordinate equations, namely: t 2 = 4 t - 3 , 7 t - 12 = t 2 , t 2 = 5 t - 6 . Each of these is a quadratic in
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Unformatted text preview: t , so each equation has two solutions: t = 1 , t = 3; t = 3 , t = 4; t = 2 , t = 3 . We see that t = 3 is the only common solution of these three equations. Therefore, the particles collide at time t = 3, at the point r 1 (3) = r 2 (3) = h 9 , 9 , 9 i ....
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