Question

Page |2 3. A marathoner runs due east for 61.5% of the time, stops and rests for 6.5% of the time, and then runs due west for remainder of the time. The average eastward velocity has magnitude 12.5 miles/hour while the average westward velocity has a magnitude of 11.0 miles per hour. Find (a) the average speed, and (b) the average velocity for the entire race. (c) How far did he run for a total time 2 hours 20 min and 24 sec? (d) What was his total displacement?

Answer 1

Total sine taken by (t) = Shows 20 min 24 sec t = 2 + 20/60 + 24/300 sec t = 2.3067 hours [1 hour = 60 min 1 hour = 3600 sec] Time taken by towards exist t_1 = 61.5% t = 61.5/100 t Time taken by for rest t_2 = 6.5% t = 6.5/100 t Time taken by him bounds best t_3 = (1 - t_1 - t_2) middot t t_3 = (1 = 61.5 - 6.5 t) t_3 = 32% t t_3 = 32/100 t Average East ward velocity (v_1) = 12.8 miles/hour. Average westward velocity (v_2) = 11 miles/hour Distance = velocity or speed/time Distance travelled towards east d_1 = v_1 h d_1 = 12.5 times 61.5/100 middot t = 12.5 times 61.5/100 times 2.3067 d_1 = 17.732 miles Distance travelled towards west d_2 = v_2 t_3 d_2 = 11 times 32/100 times t d_2 = 11 times 32/100 times 2.3037 = > d_2