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 NS 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 (FS 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.
Suppose the net vertical impulse on the 50-kg kangaroo due to all external forces was +100 N . s. Which answer below is closest to its vertical component of velocity when it leaves the ground?
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