Question

As relay runner A enters the 65-ft-long exchange zone with a speed of 30 ft/s, he begins to slow down. He hands the baton to runner B 2.5 s later as they leave the exchange zone with the same veloc- ity. Determine (a) the uniform acceleration of each of the runners, (b) when runner B should begin to run.

Answer 1

Answer:

a_a = -3.2 ft/s^2   ,   a_b = 3.723 ft/s^2

t = 5.909 s

Explanation:

Given:

  - Initial velocity of A v_i,a = 30 ft /s

  - Initial distance s_o = 0

  - Length of the exchange zone s_f = 65 ft

  - Time taken t = 2.5 s

Start out by A's velocity as he gets to the end of the exchange zone.

Part a

Runner A decelerates at a uniform rate, so you can use the equation:

                           s_f = s_o + v_i,a*t + 0.5a_a*t^2

                        65 = 0 + 30*2.5 + 0.5*a_a*2.5^2

                                   a_a = -20 / 2.5^2

                                   a _a= -3.2 ft/s^2    

Runner B accelerates at v_f,a as final velocity at a uniform rate, so you can use the equation:

                              v_f,b^2 - v_i,b^2  = 2*a_b*s

                              a_b = (30 -3.2*2.5)^2 /2*65

                                   a_b = 3.723 ft/s^2

Part b

When Runner B should begin running:

                                t = (v_f,b - v_i,b) / a_b

                               t = (30 - 3.2*2.5) / 3.723

                                        t = 5.909 s