A man jogs at a speed of 1.7 m/s. His dog waits 1.4 s and then takes off running at a speed of 3.4 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 determine how far the man and the dog will have each traveled when they meet, we need to calculate the time it takes for the dog to catch up with the man. Since the man starts jogging first and the dog starts a little later, we need to equalize the time for both of them.
Let's assume that it takes t seconds for the dog to catch up with the man.
During that time, the man will have been jogging at a constant speed of 1.7 m/s, so the distance he travels will be:
Distance_man = Speed_man * Time = 1.7 m/s * t
On the other hand, the dog waits for 1.4 seconds before taking off running at a speed of 3.4 m/s. So the distance the dog travels will be:
Distance_dog = Speed_dog * Time = 3.4 m/s * (t - 1.4 s)
For the dog to catch up with the man, the distances they travel should be equal:
Distance_man = Distance_dog
1.7 m/s * t = 3.4 m/s * (t - 1.4 s)
Now we can solve this equation for t:
1.7t = 3.4t - 3.4 * 1.4
1.7t - 3.4t = -4.76
-1.7t = -4.76
t = -4.76 / -1.7
t ≈ 2.8 seconds
Now that we have the time it takes for the dog to catch up (t ≈ 2.8 seconds), we can substitute it back into either distance equation to find the distance traveled by either the man or the dog. Let's use the distance traveled by the man equation:
Distance_man = 1.7 m/s * t
Distance_man = 1.7 m/s * 2.8 s
Distance_man ≈ 4.76 meters
Therefore, when the dog catches up with the man, the man will have traveled approximately 4.76 meters, and the dog will have traveled the same distance.