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

To determine the acceleration of each runner and when runner B should begin to run, we can use the given information about the speed and time. Using the formulas for acceleration and time, we can calculate these values.

Step-by-step explanation:

To determine the acceleration of each runner, we need to use the equation: a = (v_f - v_i) / t, where a is the acceleration, v_f is the final velocity, v_i is the initial velocity, and t is the time. Since both runners leave the exchange zone with the same velocity, their initial velocities are the same. We can use the equation to find their uniform acceleration. To find when runner B should begin to run, we need to find the time it takes for runner A to travel the length of the exchange zone, which is 65 ft, with a velocity of 30 ft/s. Using the equation t = d / v, where t is the time, d is the distance, and v is the velocity, we can find the time it takes for runner A to reach runner B.

Answer 2

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

t = 5.909 s

Step-by-step 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