Suppose a much smaller rider (total mass of rider plus pogo of \(40 \mathrm{~kg}\) ) mechanically stretched the elastic bands of the pogo by \(0.40 \mathrm{~m}\), then got on the pogo and released the bands. How high would this unwise rider go?

A. \(8.0 \mathrm{~m}\)

B. \(6.0 \mathrm{~m}\)

C. \(4.0 \mathrm{~m}\)

D. \(3.0 \mathrm{~m}\)

A new generation of pogo sticks lets a rider bounce more than 2 meters off the ground by using elastic bands to store energy. When the pogo's plunger hits the ground, the elastic bands stretch as the pogo and rider come to rest. At the low point of the bounce, the stretched bands start to contract, pushing out the plunger and launching the rider into the air. For a total mass of \(80 \mathrm{~kg}\) (rider plus pogo), a stretch of \(0.40 \mathrm{~m}\) launches a rider \(2.0 \mathrm{~m}\) above the starting point.