Question

Odysseus has returned from his epic voyage across the seas and gets off his boat at the end of a 50 meter pier. His beloved Penelope is waiting at the far side of the pier, at the origin. At the same time they see each other and race towards each other, meeting in a fierce embrace. Odysseus, exhausted from his journey, is able to run at 4 m/s, while Penelope can run at 6 m/s. Write an equation of motion for Odysseus.

Answer 1

We know that:

Distance between Odysseus and Penelope = 50m

Speed of Odysseus = So = 4m/s

Speed of Penelope = Sp = 6m/s.

Now we want to find the equation of motion for Odysseus.

First, let's find the amount of time that he is moving, we know that when he meets with Penelope, he will stop moving.

Now they weel meet each other when the total distance traveled by both of them is equal to 50m.

Then, recalling that:

Distance = Time*speed.

50m = 4m/s*t + 6m/s*t = 10m/s*t

t = 50m/10m/s = 5s

They will move for 5 seconds.

Now we can write the movement equation for Odysseus as:

p(t) = 4m/s*t + p0 for (0s ≤ t ≤ 5s)

Where p0 is the initial position of Odysseus, and because we can put our coordinate axis where we want, we can define p0 = 0m.

Then the position of Odysseus is:

P(t) = 4m/s*t if 0s ≤ t ≤ 5s

P(t) = 4m/s*5s = 20m if t > 5s.

The second piece says that for t larger than 5 seconds, he will not move (at least for a given amount of time)