A man jogs at a spee of 1.1 m/s. His dog waits 1.6s and then takes off running at a speed of 3.8 m/s to catch up with the man.
How far will they each have traveled when the dog catches up with the man?Answer in units of m
Thanks! I have one more question: how did you get the .717m for the man?
TITE
To find the distance traveled by each, we need to find the time it takes for the dog to catch up with the man.
Let's assume the time it takes for the dog to catch up with the man is "t".
Now, let's set up equations for the distance traveled by the man and the dog.
Distance traveled by the man = Speed of the man × Time taken by the man
Distance traveled by the dog = Speed of the dog × Time taken by the dog
Since the dog starts running 1.6 s after the man, the time taken by the dog is "t - 1.6" (since the dog has to cover the 1.6 s head start of the man).
Now, let's set up an equation for the distance traveled by the man and the dog:
Distance traveled by the man = 1.1 m/s × t (since the man runs at a constant speed of 1.1 m/s)
Distance traveled by the dog = 3.8 m/s × (t - 1.6) (since the dog has to cover the 1.6 s head start of the man)
Since the dog catches up with the man when they have traveled the same distance, we can set up the equation:
1.1 m/s × t = 3.8 m/s × (t - 1.6)
Now, we can solve this equation to find the value of "t" when the dog catches up with the man.
1.1t = 3.8(t - 1.6)
1.1t = 3.8t - 6.08
2.7t = 6.08
t = 6.08/2.7
t ≈ 2.253 s
Now, we can substitute the value of "t" back into the equation for the distance traveled by the man to find the distance:
Distance traveled by the man = 1.1 m/s × 2.253 s ≈ 2.48 m
Therefore, when the dog catches up with the man, they will have traveled approximately 2.48 m each.
At t = 1.6 sec., the man has jogged 1.76m.
From that point on, the dog closes in on the man at the speed of 3.8 - 1.1 = 2.7m/s.
The time for the dog to catch the man is therefore t = 1.76/2.7 = .65s.
The man will have jogged .717m further for a total distance of 2.477m.
The dog will have traveled .65(3.8) = 2.477m.