Answer to Question #193799 in Classical Mechanics for Hanan Haider

Question #193799
Two people, A and B, are running toward each other. Initially, they are 24m apart. • A starts from rest and is running with constant acceleration of 2m/s2 toward B. . B runs toward A at constant velocity of 5m/s. How far does B run in [m] until the two meet each other?
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Expert's answer
2021-05-16T17:59:48-0400

They reach each other in a time equal for both runners. Assume A runs x meters and B runs y meters:


t=2xa=yv,t=\sqrt{\frac{2x}{a}}=\frac yv,

and x+y is the total distance between them:


x+y=d.x+y=d.

Express x in terms of y:


x=dy, 2(dy)a=yv,x=d-y,\\\space\\ \sqrt{\frac{2(d-y)}{a}}=\frac yv,

re-arrange this into a quadratic equation:


y2a+2yv22vd=0, y=(2v2)+(2v2)2+4(2v2d)(a)2(a)=15 m.y^2a+2yv^2-2vd=0,\\\space\\ y=\frac{-(2v^2)+\sqrt{(2v^2)^2+4(2v^2d)(a)}}{2(a)}=15\text{ m}.

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