A runner is jogging in a straight line at a steady vr= 7 km/hr. When the runner is L= 7.6 km from the finish line, a bird begins flying straight from the runner to the finish line at vb= 28 km/hr (4 times as fast as the runner). When the bird reaches the finish line, it turns around and flies directly back to the rubber around and flies directly back to the runner.
does the bird keep turning around over and over? and so it flies 30.6km by the time the runner finishes.
Or does it just turn once. You know it flew 7.6/28 hours to get to the finish line. So now you want to know when the two met again? If it took t hours, then
7t = 7.6 - 4t
To find the distance between the runner and the bird when the bird reaches the runner, we can use the concept of relative speed.
The relative speed between the bird and the runner is the difference between their speeds. Therefore, the relative speed can be calculated as:
Relative speed = bird's speed - runner's speed
= 28 km/hr - 7 km/hr
= 21 km/hr
Now, we can determine the time it takes for the bird to reach the runner. The time can be calculated using the formula:
Time = Distance / Speed
In this case, the distance is L = 7.6 km, and the speed is the relative speed of 21 km/hr.
Time = 7.6 km / 21 km/hr
= 0.362 hours
Since the bird takes 0.362 hours to reach the runner, we can calculate the distance traveled by the bird during this time using the formula:
Distance = Speed * Time
Distance = 21 km/hr * 0.362 hours
= 7.302 km (rounded to the nearest thousandths)
Therefore, the distance between the runner and the bird when the bird reaches the runner is approximately 7.302 km.
To find the time it takes for the bird to reach the runner, we need to determine the distance between them and divide it by the bird's speed.
First, let's calculate the distance between the runner and the bird when the bird reaches the finish line. Since the bird is flying at four times the runner's speed, we can calculate the distance traveled by the bird when it reaches the finish line:
Distance = Speed × Time
D = vb × t
Since the distance between the runner and the bird is equal to the remaining distance for the runner to reach the finish line, we have:
Distance = Remaining Distance for the Runner
D = L
Rearranging the equation, we get:
t = L / vb
Substituting the given values, we have:
t = 7.6 km / 28 km/hr
Now, let's calculate the time it takes for the bird to return to the runner. Since the bird is flying at the same speed, vb, it will take the same amount of time:
t_return = t
Finally, let's calculate the total time taken by the bird:
Total Time = Time to the Finish Line + Time to Return
Total Time = t + t_return
Substituting the calculated values, we get:
Total Time = t + t
Total Time = 2t
Now, we can substitute the value of t calculated earlier:
Total Time = 2 * (7.6 km / 28 km/hr)
Performing the multiplication and division:
Total Time = 2 * 0.2714 hr
Total Time ≈ 0.5428 hr
Therefore, the total time taken by the bird to reach the runner, turn around, and return to the runner is approximately 0.5428 hours or 32.57 minutes.