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Chapter 3: Q52PE (page 124)

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 for169min at an average velocity of3.53m/s in a direction45osouth of east. What was his total displacement? (b) Allen encountered a headwind averaging2.00m/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

Expert verified

(a) The displacement covered by the person is35700meter.

(b) The average velocity relative with air speed is5.53m/s.

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

Step by step solution

01

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.

02

Given data

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

The velocity is making some angle45odegree with the x axis.

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

The gravitational acceleration is-9.8m/s2

03

Displacement of the body

a) The displacement of the body is

Vx¯=xt3.53=x10100x=3.57x104m

The displacement covered by the person is35700meter.

b) The velocity of the considering the wind

Vw=V-VairVw=3.53--2=5.53 m/s

The average velocity relative with air speed is5.53m/s.

c) Total displacement relative to the air velocity is

Vx¯=xt5.53=x10100x=5.59x104m

Total displacement relative to the air velocity is55900meter.

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Most popular questions from this chapter

Verify the ranges shown for the projectiles in Figure 3.41 (b) for an initial velocity of 50m/sat the given initial angles.

Can a goalkeeper at her/ his goal kick a soccer ball into the opponent’s goal without the ball touching the ground? The distance will be about 95m. A goalkeeper can give the ball a speed of 30m/s.

You drive \(7.50{\rm{ km}}\) in a straight line in a direction \(15^\circ \) east of north.

(a) Find the distances you would have to drive straight east and then straight north to arrive at the same point. (This determination is equivalent to find the components of the displacement along the east and north directions.)

(b) Show that you still arrive at the same point if the east and north legs are reversed in order.

Find the following for path D in Figure

(a) the total distance traveled and

(b) the magnitude and direction of the displacement from start to finish.

In this part of the problem, explicitly show how you follow the steps of the analytical method of vector addition.

The various lines represent paths taken by different people walking in a city. All blocks are \(120{\rm{ m}}\) on a side.

(a) A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a\(32^\circ \)ramp at a speed of\(40.0{\rm{ m}}/{\rm{s}}\)\(\left( {144{\rm{ km}}/{\rm{h}}} \right)\). How many buses can he clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are\(20.0{\rm{ m}}\)long?

(b) Discuss what your answer implies about the margin of error in this act—that is, consider how much greater the range is than the horizontal distance he must travel to miss the end of the last bus. (Neglect air resistance.)
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