Vanesa asked in Science & MathematicsPhysics · 11 months ago

# HELP! I don't understand this physics problem?

A runner is jogging in a straight line at a

steady vr= 2.2 km/hr. When the runner is

L= 7.1 km from the finish line, a bird begins

flying straight from the runner to the finish

line at vb= 4.4 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 is the cumulative distance the bird travels?

Update:

Part 2: 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.

Relevance
• 11 months ago

Your question does not make it clear. Is this a once round trip for the bird, or a repeated back and forth until the runner arrives at the finish line?

Let's assume that the question is as stated. Bird flies from runner to finish line and then back to runner. End of story.

Follow the bird. How long will it take the bird to reach the finish line?

speed = distance/time

rearranges to:

time = distance / speed = (7.1 km / 4.4 km/hr) = 1.61 hr

[freeze the picture]

So after 1.61 hours, we have a bird at the finish line that has flown 7.1 km and has turned around.

Meanwhile, the runner moving at half speed has only run (7.1 km/2) = 3.55 km, so he is still 3.55 km from the finish line.

[unfreeze]

Now we have a runner and a bird 3.55 km apart moving towards each other at a closing speed of

(2.2 km/hr + 4.4 km/hr) = 6.6 km/hr. How long until they meet?

time = distance / speed = (3.55 km / 6.6 km/hr) = 0.538 hr

How far has the bird flown (moving at 4.4 km/hr) in that 0.538 hr?

distance = speed * time = (4.4 km/hr * 0.538hr) = 2.367 km

Total distance flown by bird = 7.1 km + 2.367 km = 9.467 km

Say 9.5 km to two significant figures.

• Anonymous
11 months ago

The bird travels twice as fast as the runner.

When they meet again, the runner has traveled 2/3 of the 7.1 km and the bird has traveled 4/3 (3/3 out and 1/3 back) of the 7.1 km, or 9.5 km. ◄

If the bird flew 4 times as fast, then when they meet again the runner would have traveled 2/5 of the 7.1 km and the bird would have traveled 8/5 of the 7.1 km.

If the bird flew 10 times as fast, then... runner = 2/11 and bird 20/11

SO

I conclude that if the bird travels N times as fast as the runner, then when they meet again the runner has traveled 2/(N+1) of the distance and the bird has traveled 2N/(N+1)

Go back to our case -- N = 2

so runner distance = 2/(2+1) = 2/3 (of the initial distance to finish line)

and bird distance = 2*2/(2+1) = 4/3 (of the initial distance to finish line)

checks

Hope this helps!

• oubaas
Lv 7
11 months ago

A runner is jogging in a straight line at a steady Vr = 2.2 km/hr.

When the runner is Lr = 7.1 km from the finish line, a bird begins flying straight from the runner to the finish line at Vb = 4.4 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 is the cumulative distance Lb the bird travels?

Time to finish t = Lr/Vr = 7.1/2.2 h

Lb = Vb*t = 4.4*7.1/2.2 = 14.2 km

• 11 months ago

This is a standard trick question.

The runner finishes in a time of 7.1/ 2.2 hr

and in that time the bird will have flown v* t = 4.4 * 7.1/2.2 = 14.2 km

Big bird pointed out that as written the bird only does ONE return trip.

To do that consider that the bird took a time t for the trip.

In that time the runner moves forwards 2.2t

so that the bird must have flown 7.1 +(7.1-2.2t) km = 14.2-2.2t

The time taken must be distance / speed

so t = (14.2 - 2.2t) / 4.4

4.4t = 14.2-2.2t

6.6 t = 14.2

t = 14.2/6.6

the distance the BIRD flew must be 4.4 t = 4.4* 14.2/6.6 = 2/3 * 14.2 = 9.5km

Now you COULD Use this as the basis of an infinite sum of a geometric progression if you can remember your fifth form maths. To find the distance flown after each iteration.

Why not do that as a simple practice exercise?