A runner is jogging at a steady 5.2 km/hr. When the runner is 4.9 km from the finish line, a bird begins flying from the runner to the finish line at 26 km/hr (5 times as fast as the runner). When the bird reaches the finish line, it turns around and flies back to the runner.
Q1: How far does the bird travel? Even though the bird is a dodo, assume that it occupies only one point in space (a "zero" length bird) and that it can turn without loss in speed. Answer in units of km.
To calculate the distance the bird travels, we need to determine how long it takes for the bird to reach the finish line and return to the runner.
Let's first find the time it takes for the bird to reach the finish line. We can use the formula:
Time = Distance / Speed
The distance from the runner to the finish line is 4.9 km, and the speed of the bird is 26 km/hr. Plugging in these values to the formula:
Time = 4.9 km / 26 km/hr = 0.1885 hr
It takes the bird 0.1885 hours to reach the finish line.
Now, since the bird turns around and flies back to the runner, the total distance the bird travels is twice the distance from the runner to the finish line.
Distance traveled by the bird = 2 * 4.9 km = 9.8 km
Therefore, the bird travels a total distance of 9.8 km.
To find the distance the bird travels, we need to determine how long it takes for the bird to reach the finish line.
The time it takes for the bird to reach the finish line is equal to the distance between the runner and the finish line divided by the bird's speed.
Distance = 4.9 km
Speed = 26 km/hr
Time = Distance / Speed
Time = 4.9 km / 26 km/hr
Time = 0.18846153846 hr
Now, we can find the distance the bird travels by multiplying the time by the bird's speed:
Distance = Time * Speed
Distance = 0.18846153846 hr * 26 km/hr
Distance = 4.89230769231 km
Therefore, the bird travels approximately 4.892 km.