Answer to Question #193799 in Classical Mechanics for Hanan Haider

Question

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?

Answer 1

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

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

and x+y is the total distance between them:

$$x+y=d.$$

Express x in terms of y:

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

re-arrange this into a quadratic equation:

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