Question

Q1: A runner is jogging in a straight line at a steady vr= 6.8 km/hr. When the runner is L= 2.4 km from the finish line, a bird begins flying straight from the runner to the finish line at vb= 13.6 km/hr (2 times as fast as the runner). When the bird reaches the finish line, it turns around and flies directly back to the runner. What cumulative distance does the bird travel? Even though the bird is a dodo, assume that it occupies only one point in space (a “zero” length bird), travels in a straight line, and that it can turn without loss of speed. Answer in units of km. Q2: After this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. The bird repeats the back and forth trips until the runner reaches the finish line. How far does the bird travel from the beginning (including the distance traveled to the first encounter)? Answer in units of km.

Answer 1

The bird travels 1.2 km in the initial trip for Q1. For Q2, including the initial trip, the bird will travel a total distance of 4.8 km while the runner is jogging to the finish line.

Step-by-step explanation:

To solve both questions, we need to first establish how long it will take the runner to reach the finish line and then use this to determine the cumulative distance the bird would travel in that time.

Since the runner's speed is 6.8 km/hr, and the remaining distance to the finish line is 2.4 km, it would take the runner L/vr = 2.4 km / 6.8 km/hr = 0.35294117647 hours (or about 21.176 minutes) to reach the finish line.

For the first question (Q1), the bird travels directly to the finish line at 13.6 km/hr which will take it half the time of the runner, because the bird's speed is twice that of the runner. Therefore, the bird's first trip is 1.2 km. Since this is a simple back-and-forth at a constant velocity, the bird will make full trips to the runner and back to the finish line with possibly a shorter final trip when meeting the runner at the finish line.

For the second question (Q2), if we assume the bird makes its back and forth trips without any loss of time, we can calculate the total distance by adding these full trips until the time the runner finishes. However, given the bird's speed is constant and it flies back and forth without stopping, it'll be continuously flying until the runner finishes, covering a distance of 13.6 km/hr * 0.35294117647 hours = 4.8 km.

Answer 2

Q1: 3.2km

Q2: 4.8K

Step-by-step explanation:

Q1:

So db is the distance of bird, and dr is the distance of runner

db = 2vr and the distance of bird is going to be 2 times greater than the runner.

formulas: db = 2vr & db = 2dr

1. db = 2dr
2. L + (L - x) = 2x
3. 2L - x = 2x
4. 2L = 3x
5. x =
   `(2)/(3)`L

Insert it in x =
`(2)/(3)`L

`(2)/(3)`(2.4km) = 1.6km

Now we use formula db = 2dr

1. db = 2L - x
2. db = 2(2.4km) - 1.6km
3. db = 3.2km

Q2:

Formulas: Vr = L /Δt & Vb = db/Δt

1. Vr = L/ Δt ⇒ Δt =
   `(L)/(Vr)`
2. 
   `(2.4km)/(6.8km/hr)`
3. 
   `(6)/(17)hr`

(Km cancel each other)

1. Vb = db/Δt ⇒ db = VbΔt
2. 13.6km/hr
   `((6)/(17)hr )`
3. 4.8km

(hr cancel each other)

Hope it helps you :)