A hare and a tortoise compete in a race over a course 4.90 km long. The tortoise crawls straight and steadily at its maximum speed of 0.440 m/s toward the finish line. The hare runs at its maximum speed of 14.00 m/s toward the goal for 0.800 km and then stops to tease the tortoise. How close to the goal can the hare let the tortoise approach before resuming the race, which the tortoise wins in a photo finish? Assume that, when moving, both animals move steadily at their respective maximum speeds.
easy
To find the point at which the hare should resume the race, we can start by calculating the time it takes for the hare to reach the 0.800 km point.
We know the hare's speed is 14.00 m/s, and it runs for 0.800 km. To convert the distance to meters, we multiply by 1000:
0.800 km * 1000 m/km = 800 m
Next, we can use the formula t = d/v to find the time:
t = 800 m / (14.00 m/s) = 57.14 s
So it takes the hare 57.14 seconds to reach the 0.800 km point.
Now, let's find out how long it takes for the tortoise to crawl a distance that would allow the hare to finish the race at the same time.
The tortoise's speed is 0.440 m/s, and the total distance of the race is 4.90 km. To convert the distance to meters, we multiply by 1000:
4.90 km * 1000 m/km = 4900 m
Using the formula t = d/v, we find the time it takes for the tortoise to complete the race:
t = 4900 m / (0.440 m/s) = 11136.36 s
Now, we need to subtract the time taken by the hare to reach the 0.800 km point from the total time taken by the tortoise:
11136.36 s - 57.14 s = 11079.22 s
So, the hare can let the tortoise approach to a distance of 4.90 km - 0.800 km = 4.10 km before resuming the race, which the tortoise will win in a photo finish.