3.4 Cost of transport across modes of locomotion (🕒✎)

(a) You have been visiting the zoo to study the gait kinematics of kangaroos. It is very cold outside and you need to catch a train that is 2.5 km away from the zoo. It is currently 4 p.m., the closing time of the zoo, and the train leaves at 4:15 p.m. In Figure 3.18, we see the human walking speed that minimizes cost of transport is approximately 1.3 m/s (assume a cost of 3.6 J/(kg*m)) and the running speed is approximately 3.8 m/s (assume a cost of 4.2 J/(kg*m)). What is the most energy efficient combination of walking and running at these optimal speeds that will allow you to catch your train? What is the total cost, rounded to the nearest kilojoule (assume your mass is 70 kg)? You must leave the zoo immediately because it is closing, and you cannot stop for more than two minutes during your journey because you will get too cold.

(b) Now let’s say that the zoo has allowed you to take a kangaroo home as a pet. You have to keep up with your new pet, so the kangaroo can use a hopping speed of at most 5 m/s with a cost of transport of 3.8 J/(kg*m) or a pentapedal gait at 1.6 m/s with a cost of transport of 15 J/(kg*m). What is the most energy efficient combination of a hopping and pentapedal gait for your kangaroo (to catch the train without stopping for more than two minutes, as above)?