Question

In reaching her destination, a backpacker walks with an average velocity of 1.17 m/s, due west. This average velocity results, because she hikes for 5.57 km with an average velocity of 3.24 m/s due west, turns around, and hikes with an average velocity of 0.486 m/s due east. How far east did she walk (in kilometers)?

Answer 1

Consider west as positive direction of motion and east as negative direction of motion

V_avg = average velocity = 1.17 m/s

D_w = distance traveled in west direction = 5.57 km = 5570 m

v_w = average velocity to travel distance in west direction = 3.24 m/s

t_w = time of travel in west direction = D_w /v_w = 5570/3.24 = 1719.14 sec

D_E = distance traveled in east direction = ?

v_E = average velocity to travel distance in east direction = - 0.486 m/s

t_E = time of travel in east direction = D_E /v_E

Average velocity is given as

V_avg = Total displacement/total time

V_avg = (D_w - D_E ) /(t_w + t_E )

1.17 = (5570 - D_E ) /(1719.14 + D_E /0.486)

D_E = 1044.4 m

D_E = 1.044 km