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 45° south of east. what was his total displacement? (enter the magnitude in km and the direction in degrees south of east.) magnitude km direction ° south of east (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? (enter the magnitude in m/s and the direction in degrees south of east.) magnitude m/s direction ° south of east (c) what was his total displacement relative to the air mass? (enter the magnitude in km and the direction in degrees south of east.) magnitude km direction ° south of east

(a) 3.58 km 45° south of east

The total displacement is given by:

where

v is the average velocity

t is the time

The average velocity is:

v = 3.53 m/s

While we need to convert the time from minutes to seconds:

Therefore, the magnitude of the displacement is

And the direction is the same as the velocity, therefore 45° south of east.

(b) 5.53 m/s 90° south of east

The velocity of the air relative to the ground is

and the direction is exactly opposite to that of Allen, so it is 45° north of west. Allen's velocity relative to the ground is

v = 3.53 m/s

So this must be the resultant of Allen's velocity relative to the air (v') and the air's speed (). Since these two vectors are in opposite direction, we have

Therefore we find v', Allen's velocity relative to the air:

The direction must be measured relative to the air's reference frame. In this reference frame, Allen is moving exactly backward, so his direction will be 90° south of east.

(c) 56.1 km at 90° south of east.

Since Allen's velocity relative to the air is

v' = 5.53 m/s

Then the displacement of Allen relative to the air will be given by

and substituting,

And the direction is the same as that of the velocity, therefore will be 90° south of east.

gravity

explanation: