• Aucun résultat trouvé

Épreuve de section européenne A

N/A
N/A
Info
Télécharger
Protected

Academic year: 2022

Partager "Épreuve de section européenne A"

Copied!
1
0
0

Chargement.... (Voir le texte intégral maintenant)

Texte intégral

(1)

2013 – 32 Felix Baumgartner’s skydive

Baccalauréat, Série S Session de juin 2013

Épreuve de section européenne

A mathematical analysis of Felix Baumgartner’s skydive

On Sunday, October 14th, 2012, Austrian skydiver Felix Baumgartner broke the world records for highest manned balloon flight, highest skydive, and greatest speed achieved without vehicular power. He rode the Red Bull Stratos helium balloon to a height of

39,045

meters above New Mexico before free falling in a pressure suit and parachuting back to the ground. He reached a maximum velocity of

1,342

kilometers per hour after falling for

42

seconds, becoming the first person to travel faster than sound without vehicular power. The free fall lasted

4

minutes and

20

seconds before Baumgartner pulled his parachute.

Now let us compare what happened with the theoretical calculations of what should have happened.

The gravitational attraction felt by Baumgartner was roughly g9.7026 m.s2 when he started his free fall. The velocity formula v t( )v initial( )g t. gives a velocity after

42

seconds of

407.5

meters per second (

1,467

kilometers per hour).

This is

9.3%

faster than Baumgartner's actual maximum velocity.

From a text written by Matthew Reece http://www.examiner.com/article/a-mathematical-analysis-of-felix-baumgartner-s-skydive

Questions

1. Check that

1,342

kilometers per hour is about

372.8

meters per second.

2. Why do we obtain a result that is “faster than Baumgartner's actual maximum velocity”?

3.

a. “The velocity formula v t( )v initial( )g t. gives a velocity after

42

seconds of

407.5

meters per second”. Check that result.

b. The distance covered in t seconds is given by the formula: 1

( ) . ²

d t  2g t . Compute the distance between Felix's position at the beginning of his jump, and his position after the

42-

second free fall.

c. Explain the link between g , v t( ) , and d t( ).

Références

Télécharger maintenant ( PDF - 1 Page - 239.46 KB )

Documents relatifs

Épreuve de section européenne

Draw a trigonometric circle to show that the cosine function is even and that the sine function is odd.. Prove that any polynomial function of x that contains only even powers of x

Épreuve de section européenne

The values of x corresponding to assigned values of y always occur in pairs equal in mag- nitude 1 and opposite in sign, since the equation only contains even powers of x; therefore

Épreuve de section européenne

Since the area of the original big white square is exactly equal to the total area of the light grey squares, the area of the region that’s covered twice must be exactly equal to

Épreuve de section européenne

The lazy caterer’s 1 sequence, more formally known as the cen- tral polygonal numbers, describes the maximum number of pieces of a circle (a pancake is usually used to describe

Épreuve de section européenne

Sometimes it is easier to prove a result in the contrapositive form rather than in the original conditional form : for instance “if the square of a natural number is not odd, then

Épreuve de section européenne

Of course, it doesn’t work all the time with division: a Gaussian integer a is said to be divisible by another one b if there exists another Gaussian integer c such that bc = a1.

Épreuve de section européenne

Triangular numbers A triangular number gives the number of dots that can form an equilateral triangle, as in the diagram on the right.. The n -th triangular number T n is the number

Épreuve de section européenne

Prove that the number x given at the end of the Chinese Remainder Theorem text is solution to the system ( S ). 2012-25 – Chinese