Bryan Allen pedaled a human-powered aircraft across the English Channel from the cliffs of Dover to Cap Gris-Nez on June 12, 1979. (a) He flew for 169 min at an average velocity of 3.53 m/s in a direction 45º south of east. What was his total displacement? (b) Allen encountered a headwind averaging 2.00 m/s almost precisely in the opposite direction of his motion relative to the Earth. What was his average velocity relative to the air? (c) What was his total displacement relative to the air mass?

Solution to 52PE

Step 1 of 3</p>

We need to find the total displacement of Bryan while he was crossing the English Channel with an average velocity of 3.53m/s along south of east for 169 minutes. We also need to compute the average velocity of Bryan relative to air if he encounters a headwind of 2m/s in direction opposite to his motion. The total displacement relative to the air mass also have to be calculated.

To compute the above mentioned parameters, we need to resolve the velocity vector into its components.

The components of velocity are as follows:

Where is the velocity relative to earth in east direction.

Step 2 of 3</p>

(a)

Time, =169 minutes

=10140s

is the given velocity.

We know that,

is the displacement

Thus the displacement is