Question

A cheetah can maintain its maximum speed of 100 km/hr for 30.0 seconds. What minimum distance must a gazelle running 80.0 km/hr be ahead of the cheetah to escape?

Answer 1

Explanation:

Suppose the cheetah is initially positioned at x=0 (m) from the reference, and the gazelle is intially at poisiton x=d (m).

Then, at the worst case, that is when cheetah is running at the maximum case, the position of the gazelle relative to the reference must be larger than that of cheetah.

In equation form,

$0\text{ km}+\frac{100\text{ km}}{1 \text{ hr}}\cdot30\text{ s }\cdot\frac{1\text{ hr}}{3600\text{ s}}\le d \text{ km}+\frac{80\text{ km}}{1 \text{ hr}}\cdot30\text{ s }\cdot\frac{1\text{ hr}}{3600\text{ s}}$

$(100-80)\cdot \frac{30}{3600}\le d$

$d\ge \frac16\text{ km}=166.66 \text{m}$