A cat is being chased by a dog. Both are running in a straight line at constant speeds. The cat has a head start of 3.6 m. The dog is running with a speed of 8.9 m/s and catches the cat after 6.9 s. How fast did the cat run?
To determine how fast the cat ran, we can use the formula for calculating speed: speed = distance / time.
We know that the dog catches the cat after 6.9 seconds, so the time taken by the cat is also 6.9 seconds. Let's denote the speed of the cat as 'v' ( to be determined).
We also know that the dog's speed is 8.9 m/s.
The cat has a head start of 3.6 meters, which means the distance covered by the cat is the distance between the cat and the dog when the dog catches up.
So, the distance covered by both the cat and the dog is the same when the dog catches the cat.
The distance covered by the cat is the product of its speed and time: d_cat = v * 6.9
The distance covered by the dog is the distance it traveled in 6.9 seconds, which is the speed of the dog multiplied by time: d_dog = 8.9 * 6.9
Since both distances are the same, we can equate them:
v * 6.9 = 8.9 * 6.9
Now we can solve for v by dividing both sides of the equation by 6.9:
v = (8.9 * 6.9) / 6.9
Simplifying the equation:
v = 8.9
Therefore, the cat ran at a speed of 8.9 m/s.