Chapter 7, Problem 93RPP

BIO Kangaroo hopping Hopping is an efficient method of locomotion for the kangaroo (see Figure 7.18). When the kangaroo is in the air, the Earth-kangaroo system has a combination of gravitational potential energy and kinetic energy. When the kangaroo lands, its Achilles tendons and the attached muscles stretch-a form of elastic potential energy. This elastic potential energy is used along with additional muscle tension 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 horizontal and vertical force components exerted by a firm surface on a kangaroo’s feet while it hops are shown in Figure 7.19a. the vertical force N_{S on k y} (Figure 7.19b) 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 gravitational force that Earth exerts on the kangaroo. The surface exerts a backward horizontal force (F_{S on K z}) on the kangaroo’s foot while it lands and a forward horizontal force as it pushes off for the next hop (Figure 7.19c), similar to what happens to a human foot when landing in front 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? Assume that the kangaroo is initially at rest.

a. +2.0 m/s

b. +3.0 m/s

c. +4.0 m/s

d. +8.0 m/s

e. +10 m/s