Lets choose coordinate system so that cheetah is at the origin of x-axis and gazelle L meters ahead.
The equations of motion of cheetah and gazelle are xC(t)=vCt, xG(t)=vGt+L respectively, where vC=92hkm , vG=72.7hkm, L=72.9m. When cheetah catches the gazelle, xC(t)=xG(t), from where vCt=vGt+L⇒t=vC−vGL≈13.6s.
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If both animals are running at full speed, with the gazelle 55.1 m ahead, how long before the cheetah catches its prey? Answer in units of s.