Answer to Question #96042 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.

Answer 1

Speeds of animals

$v_c=92\:\rm km/h=25.6 \:\rm m/s$

$v_g=72.7\:\rm km/h=20.2 \:\rm m/s$

The relative speed of the cheetah with respect to gazelle

$$v=v_c-v_g=25.6\:\rm m/s-20.2\: m/s=5.4\: m/s$$

Therefore, the time when the cheetah catches its prey

$$t=\frac{d}{v}=\frac{72.9\:\rm m}{5.4\:\rm m/s}=13.5\:\rm s$$