A man jogs at a speed of 1.7 m/s. His dog waits 1.9 s and then takes off running at a speed of 2.7 m/s to catch the man.
How far will they have each traveled when the dog catches up with the man?
Answer in units of m
To find the distance traveled by the man and the dog when they meet, we can use the concept of relative speed.
First, let's determine the time it takes for the dog to catch up with the man. We can set up an equation based on the relative speeds of the dog and the man:
Relative speed = Dog's speed - Man's speed
Relative speed = 2.7 m/s - 1.7 m/s = 1.0 m/s
Now, we need to find the time it takes for the dog to catch up with the man. We can use the equation:
Distance = Speed × Time
Since we know the relative speed is 1.0 m/s and the dog waits for 1.9 s before taking off, the time it takes for the dog to catch up with the man can be calculated as:
Time = 1.9 s
Now, we can use the equation Distance = Speed × Time to find the distance traveled by the dog:
Distance (dog) = 2.7 m/s × 1.9 s = 5.13 m
Similarly, we can find the distance traveled by the man using the given speed and time:
Distance (man) = 1.7 m/s × 1.9 s = 3.23 m
Therefore, the dog and the man will have each traveled approximately 3.23 m and 5.13 m respectively when they meet.