Question

A cheetah can run at a maximum speed 101 km/h and a gazelle can run at a maximum speed of 78.4 km/h. If both animals are running at full speed, with the gazelle 82.7 m ahead, how long before the cheetah catches its prey? Answer in units of s.

Answer 1

To determine how long it takes for the cheetah to catch the gazelle, we can start by calculating their speeds in meters per second (m/s):

1. **Convert the speeds from km/h to m/s**:
\[
\text{Cheetah's speed} = 101 \text{ km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} = \frac{101 \times 1000}{3600} \approx 28.06 \text{ m/s}
\]

\[
\text{Gazelle's speed} = 78.4 \text{ km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} = \frac{78.4 \times 1000}{3600} \approx 21.78 \text{ m/s}
\]

2. **Determine the relative speed**:
\[
\text{Relative speed} = \text{Cheetah's speed} - \text{Gazelle's speed} = 28.06 \text{ m/s} - 21.78 \text{ m/s} = 6.28 \text{ m/s}
\]

3. **Determine the initial distance between them**: The gazelle is 82.7 m ahead of the cheetah.

4. **Calculate the time it takes for the cheetah to catch the gazelle**:
Using the formula time = distance / speed:
\[
\text{time} = \frac{\text{distance}}{\text{relative speed}} = \frac{82.7 \text{ m}}{6.28 \text{ m/s}} \approx 13.15 \text{ s}
\]

Thus, the time it takes for the cheetah to catch the gazelle is approximately \(\boxed{13.15}\) seconds.