Question

Bryan Allen pedaled a humanpowered aircraft across the English Channel from the cliffs of Dover to Cap GrisNez 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?

Bryan Allen's total displacement is approximately:
a) 500 km
b) 1000 km
c) 1500 km
d) 2000 km

Answer 1

To find Bryan Allen's total displacement, we can use the horizontal and vertical components of his average velocity. The horizontal displacement is equal to the horizontal component of the average velocity multiplied by the time of flight. The vertical displacement is zero.

Step-by-step explanation:

To find Bryan Allen's total displacement, we can break down his motion into its horizontal and vertical components. First, let's find the horizontal displacement. We can use the average velocity and the time of flight given. The horizontal component of the average velocity can be found by multiplying the average velocity by the cosine of the angle south of east:

Horizontal component of average velocity = 3.53 m/s * cos(45°) = 2.50 m/s

The horizontal displacement is then given by multiplying the horizontal component of the average velocity by the time of flight:

Horizontal displacement = 2.50 m/s * 169 min

Next, let's find the vertical displacement. The vertical component of the average velocity can be found by multiplying the average velocity by the sine of the angle south of east:

Vertical component of average velocity = 3.53 m/s * sin(45°) = 2.50 m/s

Since the vertical component of the average velocity is zero, the vertical displacement is zero.

Therefore, the total displacement of Bryan Allen is equal to the horizontal displacement, which is the answer to part (a) of the question.