Answer to Question #96184 in Physics for sarah

Question

A cheetah can run at a maximum speed
92 km/h and a gazelle can run at a maximum speed of 72.7 km/h.
If both animals are running at full speed,
with the gazelle 72.9 m ahead, how long before
the cheetah catches its prey?
Answer in units of s. Don't round answer.

Answer 1

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 $x_C(t) = v_C t$, $x_G(t) = v_G t + L$ respectively, where $v_C = 92 \frac{km}{h}$ , $v_G = 72.7 \frac{km}{h}$, $L = 72.9 m$. When cheetah catches the gazelle, $x_C(t) = x_G(t)$, from where $v_C t = v_G t + L \Rightarrow t = \frac{L}{v_C - v_G} \approx 13.6 s$.