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Benjamin Bertrand
2017-06-16 09:49:23 +03:00
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% origin: Asie Juin 2015 exercice 2
% theme: QCM, fraction, grandeurs, pourcentage
Rémi s'est inscrit à son premier triathlon \og distance olympique \fg.
Il devra effectuer : 1,5 km de natation, puis 40 km de cyclisme, puis 10 km de course à pied.
Il a reçu les informations suivantes (Les deux schémas ne sont pas à l'échelle):
\medskip
\parbox{0.6\linewidth}{
\textbf{Natation:} \\
Partir du point D, rejoindre la bouée A à 250 m du départ, la contourner à 900 sur la gauche, aller jusqu'à la bouée B, la contourner encore à gauche et rejoindre le point de départ D qui est à 650 m de la bouée B.}\hfill
\parbox{0.3\linewidth}{
\includegraphics[scale=1]{./fig/Sept_2012_Metro_PB_nage}
}
\medskip
\parbox{0.6\linewidth}{
\textbf{Cyclisme:} \\
Départ au point P au pied du col, montée régulière de 20 km jusqu'au sommet S du col avec un dénivelé de 800 m, puis descente par la même route et retour au point P.}
\hfill
\parbox{0.3\linewidth}{
\includegraphics[scale=1]{./fig/Sept_2012_Metro_PB_deniv}
}
\medskip
\textbf{Course à pied} \\
Circuit de 5 km à parcourir 2 fois.
\medskip
\begin{enumerate}
\item Partie natation
Rémi prévoit de parcourir 1~km toutes les 20~minutes.
Expliquer pourquoi, s'il nage régulièrement, il devrait mettre 30minutes pour la partie natation.
\item Partie cyclisme
\begin{enumerate}
\item Vérifier par un calcul que la valeur arrondie au mètre près de PH est 19 984 mètres.
\item Rémi sait qu'avec une telle pente il peut prévoir 1 h 30 min pour cette subpartie du triathlon.
\medskip
\fbox{
\parbox{0.5\linewidth}{La pente moyenne $p$ d'une route est un pourcentage qui se calcule de la façon suivante :
\[p = \dfrac{d}{l} \times 100\]
où $d$ et $l$ sont exprimées dans la même unité.}\hfill
\parbox{0.4\linewidth}{
\includegraphics[scale=1]{./fig/Sept_2012_Metro_PB_pente}
}}
\medskip
Calculer la pente moyenne du col que doit escalader Rémi.
\end{enumerate}
\item Partie course à pied
Pour la dernière partie de son triathlon, Rémi prévoit de mettre 20~minutes pour chacun des deux tours du circuit de 5~km.
Déterminer en km/h sa vitesse moyenne pour la course à pied s'il respecte ses prévisions.
\item Totalité du triathlon
Recopier puis completer le tableau suivant \textit{(les temps seront donnés en heures et en minutes)}.
\begin{tabular}{|c|*{4}{p{2.6cm}|}}
\hline
Épreuve & Natation & Cyclisme & Course à pied & Total \\
\hline
Temps prévus & & 1h30min & & \\
\hline
\end{tabular}
\end{enumerate}
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