Question

a cheetah can run approx 100km/hr and a gazelle at 80km/hr , if both animals are running at full speed with gazelle 60m ahead.how long before cheetah catches its prey?

Answer 1

A cheetah can run approx 100km/hr and a gazelle at 80km/hr, if both animals are running at full speed with gazelle 60m ahead. How long before cheetah catches its prey?

Solution:

$$V = 100 \frac{km}{hr} = \frac{250m}{9s} - speed\ of\ the\ cheetah;$$ $$U = 80 \frac{km}{hr} = \frac{200m}{9s} - speed\ of\ the\ gazelle;$$ $$S = 60m - the\ distance\ between\ the\ animals$$

Cheetah's relatively to the speed of gazelle:

$$\begin{array}{l} x: V_{c \rightarrow g} = V_{c} - V_{g} = V - U = \frac{250m}{9s} - \frac{200m}{9s} \\ = \frac{50m}{9s} \end{array}$$

Now the gazelle is fixed and cheetah runs with speed $V_{c \rightarrow g} = \frac{50m}{9s}$. Time after which the cheetah will catch the gazelle:

$$t = \frac{S}{V_{c \rightarrow g}} = \frac{60m}{\frac{50m}{9s}} = \frac{9 \cdot 60m \cdot s}{50m} = 10.8s$$

Answer: Time after which the cheetah will catch the gazelle $t = 10.8s$.