Okay, I have an example problem that I'm trying to solve that comes with the answer; I'm just trying to figure out what to do.
A man jogs at a speed of 1.8 m/s. His dog
waits 2 s and then takes off running at a speed
of 4 m/s to catch the man.
How far will they have each traveled when
the dog catches up with the man?
Correct answer: 6.54545 m.
I think that I'll need to set the two equations equal and that I see that I'm given time and two sets of constant velocity but I looked at all my equations that I have and I can't figure out what equation I need.
Any help would be welcome.
V=d/t
d=V*t
Let t be the time the man is jogging. t-2 is the time the dog is running (since the dog waits 2s). When they catch up with each other displacement will be equal.
(4m/s)(t-2)=(1.8m/s)(t)
To solve this problem, you can start by setting up two equations based on distance, time, and velocity for the man and the dog. Let's assume that both the man and the dog start at the same position at time t = 0.
Equation for the man:
Distance traveled by the man = velocity of the man * time taken by the man
Equation for the dog:
Distance traveled by the dog = velocity of the dog * (time taken by the dog - 2 seconds)
Since both the man and the dog have to reach the same point when the dog catches up, the distances traveled by both should be equal. Therefore, we can set up the following equation:
velocity of the man * time taken by the man = velocity of the dog * (time taken by the dog - 2 seconds)
Now, let's plug in the values we have:
Man's velocity = 1.8 m/s
Dog's velocity = 4 m/s
Time taken by the dog = time taken by the man + 2 seconds (since the dog waits for 2 seconds before starting)
Let's assume the time taken by the man to be t seconds. Therefore, the time taken by the dog would be t + 2 seconds.
Now we can substitute these values into the equation:
1.8 * t = 4 * (t + 2)
Next, you can solve this equation for t to find the time taken by the man. Once you have the value of t, you can substitute it back into either equation to find the distance traveled by both the man and the dog.
In this case, the correct answer is given as 6.54545 m, which means when you solve the equation correctly, you will get t ≈ 2.534 m.
Thus, when the dog catches up with the man, the man will have traveled approximately 2.534 m, and the dog will have traveled approximately 6.54545 m.