How far apart are the dog and cat after 30 meters? - briefly
After traveling 30 meters, the distance between the dog and the cat is determined by their initial separation and any changes in their relative positions during the movement. The exact distance depends on whether they maintain a constant separation or if one of them has accelerated or decelerated.
How far apart are the dog and cat after 30 meters? - in detail
To determine how far apart the dog and cat are after traveling 30 meters, we must consider their respective speeds and the duration of their movement. Let's assume both animals start from the same point and move in the same direction.
Firstly, let's establish typical average speeds for a domestic dog and cat:
- A dog might run at an average speed of about 20 kilometers per hour (km/h).
- A cat, being smaller and less efficient in long-distance running, might average around 10 km/h.
Next, we convert these speeds into meters per second (m/s) for easier calculation:
- Dog's speed: ( \frac{20 \text{ km/h}}{3600} = \frac{20000}{3600} \approx 5.56 \text{ m/s} )
- Cat's speed: ( \frac{10 \text{ km/h}}{3600} = \frac{10000}{3600} \approx 2.78 \text{ m/s} )
Now, we calculate the time each animal takes to cover 30 meters:
- Time for the dog: ( t_{\text{dog}} = \frac{\text{distance}}{\text{speed}} = \frac{30 \text{ m}}{5.56 \text{ m/s}} \approx 5.4 \text{ seconds} )
- Time for the cat: ( t_{\text{cat}} = \frac{\text{distance}}{\text{speed}} = \frac{30 \text{ m}}{2.78 \text{ m/s}} \approx 10.8 \text{ seconds} )
Given that the dog is faster, it will have covered more distance in the time it takes the cat to travel 30 meters. To find out how far apart they are after the cat has traveled 30 meters:
- Distance traveled by the dog in 10.8 seconds: ( d{\text{dog}} = \text{speed} \times t{\text{cat}} = 5.56 \text{ m/s} \times 10.8 \text{ s} \approx 60.13 \text{ meters} )
Therefore, after the cat has traveled 30 meters, the dog will be approximately ( 60.13 - 30 = 30.13 \text{ meters} ) ahead of the cat. This detailed analysis provides an accurate measure of the distance between the two animals under the given conditions.