A cheetah can run at a maximum speed
96.6 km/h and a gazelle can run at a maximum speed of 78.5 km/h.
If both animals are running at full speed,
with the gazelle 93.9 m ahead, how long before
the cheetah catches its prey?
Answer in units of s.
keeping all distances in km,
96.6x = 78.5x + 0.0939
now change that to seconds
To find the time it takes for the cheetah to catch the gazelle, we can first convert the speeds of both animals to meters per second.
Given:
Cheetah's speed = 96.6 km/h
Gazelle's speed = 78.5 km/h
To convert km/h to m/s, we can use the conversion factor, which is 1 km/h = 0.2778 m/s.
Cheetah's speed in m/s = 96.6 km/h * 0.2778 m/s = 26.83 m/s
Gazelle's speed in m/s = 78.5 km/h * 0.2778 m/s = 21.8 m/s
Now, we can find the relative speed between the cheetah and the gazelle, which is the difference in their speeds.
Relative speed = Cheetah's speed - Gazelle's speed = 26.83 m/s - 21.8 m/s = 5.03 m/s
Since the gazelle is initially 93.9 m ahead, the cheetah needs to cover this distance to catch up.
Therefore, the time it takes for the cheetah to catch the gazelle can be calculated using the formula:
Time = Distance / Speed
Time = 93.9 m / 5.03 m/s ≈ 18.67 seconds
Hence, it will take approximately 18.67 seconds for the cheetah to catch its prey.