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,

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

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

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

Answer 2

The minimum distance that a gazelle running 80.0 km/hr be ahead of the cheetah to escape is 6.5807km

If a cheetah can maintain its maximum speed of 100 km/hr for 30.0 seconds, the distance covered by the cheetah is expressed as:

Distance  = Speed * time

Given the following:

• Speed = 100km/hr

• Time = 30secs = 0.00833333hr

Distance covered = 100 * 0.00833333

Distance covered = 0.0833 km

If gazelle is running at a speed of 80.0km/hr, the distance of gazelle will be expressed as:

• Distance of gazelle = 80 * 0.08333

• Distance covered by gazelle = 6.6664km

Taking the difference in distance = 6.6664km - 0.0833 km =6.5807km

Hence the minimum distance that a gazelle running 80.0 km/hr be ahead of the cheetah to escape is 6.5807km

Learn more on speed here: https://brainly.com/question/24732604