Kangaroo hopping Hopping is an efficient method of locomoti for the kangaroo (see F...

Kangaroo hopping Hopping is an efficient method of locomoti for the kangaroo (see Figure 6.14). When the kangaroo is in the air, the Earth-kangaroo system has a combinati of gravitati al potential energy and kinetic energy. When the kangaroo lands, its Achilles tend s and the attached muscles stretch—a form of elastic potential energy. This elastic potential energy is used al g with additi al muscle tensi to launch the kangaroo off the ground for the next hop. In the red kangaroo, more than 50% of the total energy used during each hop is recovered elastic potential energy. This is so efficient that the kangaroo’s metabolic rate actually decreases slightly as its hopping speed increases from 8 km/h to 25 km/h.

The horiz tal and vertical force comp ents exerted by a firm surface a kangaroo’s feet while it hops are shown in Figure 6.15a. The vertical force N_S K (Figure 6.15b) varies: when the kangaroo is not touching the surface S, the force is zero; when it is pushing off, the force is about three times the gravitati al force that Earth exerts the kangaroo. The surface exerts a backward horiz tal force (F_S K x ) the kangaroo’s foot while it lands and a forward horiz tal force as it pushes off for the next hop (Figure 6.15c), similar to what happens to a human foot when landing in fr t of the body and when pushing off for another step when behind the body.

Which answer below is closest to the vertical impulse that the ground exerts on the kangaroo while it takes off?