Question

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${45}^o$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?

Short answer

(a) The displacement covered by the person is$35700$meter.

(b) The average velocity relative with air speed is$5.53$m/s.

(c) Total displacement relative to the air velocity is $55900$meter.

Step-by-step solution

Definition of velocity

The directional speed of an item in motion is an indication of its rate of change in position as seen from a specific point of view and measured by a specific time standard.

Given data

The velocity can be said as is $3.53$m/s.

The velocity is making some angle${45}^o$degree with the x axis.

The time taken by him is $169$min, which can be converted into seconds

The gravitational acceleration is$-9.8$m/s²

Displacement of the body

a) The displacement of the body is

$\begin{array}{rcl}\overline{V_x}& =& \frac{x}{t}\\ 3.53& =& \frac{x}{10100}\\ x& =& 3.57x{10}^{4}m\\ & & \end{array}$

The displacement covered by the person is$35700$meter.

b) The velocity of the considering the wind

$\begin{array}{rcl}{V}_w& =& V-V_{air}\\ V_w& =& 3.53-\left(-2\right)\\ & =& 5.53 m/s\\ & & \end{array}$

The average velocity relative with air speed is$5.53$m/s.

c) Total displacement relative to the air velocity is

$\begin{array}{rcl}\overline{V_x}& =& \frac{x}{t}\\ 5.53& =& \frac{x}{10100}\\ x& =& 5.59x{10}^{4}m\\ & & \end{array}$

Total displacement relative to the air velocity is$55900$meter.