A man jogs along at 1.2 m/s. His dog, playing 36 m behind him, waits for 5 s, then takes off after him at 3.1 m/s.
How far apart are they when the dog starts
after his master?
Answer in units of m.
If the man continues jogging, how long will
the dog have to run to catch up to his master?
Answer in units of s.
How far will the dog run?
How far will the dog run?
To find the distance between the man and the dog when the dog starts after his master, we can use the formula:
Distance = Speed × Time
Given:
Man's speed = 1.2 m/s
Delay time = 5 s
Distance the dog waits = 36 m
Distance the man runs during the delay = Man's speed × Delay time
= 1.2 m/s × 5 s
= 6 m
Initial distance between man and dog = Distance the dog waits + Distance the man runs during the delay
= 36 m + 6 m
= 42 m
Therefore, when the dog starts after his master, they are 42 meters apart.
To find how long the dog will have to run to catch up to his master, we can use the formula:
Time = Distance / Relative Speed
Relative speed = Dog's speed - Man's speed
= 3.1 m/s - 1.2 m/s
= 1.9 m/s
Distance the dog has to cover = Initial distance between man and dog
= 42 m
Time the dog takes to catch up = Distance the dog has to cover / Relative speed
= 42 m / 1.9 m/s
≈ 22.1 s
Therefore, the dog will have to run for approximately 22.1 seconds to catch up to his master.
To find how far the dog will run, we can use the formula:
Distance = Speed × Time
Given:
Dog's speed = 3.1 m/s
Catch-up time = 22.1 s
Distance the dog runs = Dog's speed × Catch-up time
= 3.1 m/s × 22.1 s
≈ 68.51 m
Therefore, the dog will run approximately 68.51 meters.
To find the distance between the man and the dog when the dog starts running, we need to determine how far the man has jogged during the time the dog is waiting.
The dog waits for 5 seconds, during which the man is jogging at a speed of 1.2 m/s. Therefore, the distance the man has jogged is given by:
Distance = Speed × Time = 1.2 m/s × 5 s = 6 meters.
Therefore, when the dog starts running, it is 6 meters behind the man.
Now, let's find out how long the dog will have to run to catch up to his master. We can set up an equation of the form:
Distance = Speed × Time.
Since we are looking for the time the dog runs until it catches up to the man, we can represent this time as 't'.
For the dog to catch up, the distance it travels must be equal to the distance the man has already jogged plus any additional distance covered by the dog.
The distance the dog travels is given by:
Distance = Speed × Time = 3.1 m/s × t.
The distance the man jogs, which needs to be covered by the dog, is 6 meters.
Therefore, we have the equation: 6 meters + 3.1 m/s × t = 1.2 m/s × t.
Solving this equation, we can determine the value of 't'.
6 meters + 3.1 m/s × t = 1.2 m/s × t
6 meters = 1.2 m/s × t - 3.1 m/s × t
6 meters = (1.2 m/s - 3.1 m/s) × t
6 meters = -1.9 m/s × t
t = 6 meters / -1.9 m/s
t ≈ -3.16 seconds
Since time cannot be negative, we can conclude that the dog cannot catch up to the man running at these speeds.
Therefore, the dog will not be able to catch up to his master.
Hence, the distance the dog will run is indefinite.
How far does the man run in 5 s? That would be 1.2*5 = 6 meters. You have to add that to 36 meters, which was the initial distance the dog was behind. That makes 42 m makeup distance.
The intervening distance gets reduced at a rate 3.1 - 1.2 = 1.9 m/s
The dog catches up after
t = 42/1.9 = 22.1 s