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Relative velocity: Boat problems

Problem 1. 

A river  flows due East at a speed of 1.3 metres per second. A girl in a rowing boat, who can row at 0.4 metres per second in still water, starts from a point on the South bank and steers due North. The boat is also blown by a wind with speed 0.6 metres per second from a direction of N20ºE.


Find the resultant velocity of the boat and its magnitude.If the river has a constant width of 10 metres, how long does it take the girl to cross the river, and how far upstream or downstream has she then travelled?

Problem 2. 

A river  flows due West at a speed of 2.5 metres per second and has a constant width of 1 km. You want to cross the river from point A (South) to a point B (North) directly opposite with a motor boat that can manage to a speed of  5 metres per second.

If you head out pointing your boat at an angle of 90 degrees to the bank. How long does it take to get from point A to point B?After crossing the river you realised that it took  longer than expected. In what direction…

Graphical representation of the domain and range of real functions

A function specifies a rule by which an input is converted to a unique output.

More precisely:

A function $f$ is a rule that assigns to each element $x$ in a set $D$ exactly one element, called $f(x)$, in a set $E$.

The domain of a function is the set of all possible $x$ values that can be used as inputs, and the range is the set of all possible $f(x)$ values that arise as outputs.

It's helpful to think of a function as a machine (see Figure 1). If $x$ is in the domain of the function then when enters the machine, it is accepted as an input and the machine produces an output according to the rule of the function. Thus we can think of the domain as the set of all possible inputs $x$ and the range as the set of all possible outputs  $f(x)$.

The most common method for visualising a function is its graph; which consists of all points $(x,y)$ in the coordinate plane such  that  $y=f(x)$ and $x$ is in the domain of $f$.

The graph of a function $f$ gives us a useful picture of the behavi…

A geometrical approach to the concepts of speed and acceleration (Part I)

1. Introduction

1.1 The concepts of speed and acceleration
How good is your understanding of speed and acceleration? Would it stand up under cross-examination in court? Here are some questions that you might be asked by a court prosecutor to test your credibility as an expert witness:
1.Speed is understood as distance divided by time. What distance is being referred to here? What time is being referred to here?
2.Is this what your car’s speedometer is measuring when it registers, for example, 60 km/hr? To what distance and time would it be referring?
3.Until the introduction of digital technology in the 1980s, cars used eddy current speedometers (you can google this). Did these measure any actual distances and times? What did they measure?
4.How would you measure the change in speed of a vehicle?
5.What do you think acceleration means? (‘Getting faster’ isn’t an expert answer and would reflect badly on your credibility. You would be expected to give a numerical definition.)
1. 2 Galileo…

Breve Tabla Cronológica de la Historia de las Matemáticas (Actualizada)

El documento que aquí comparto contiene información actualizada con vínculos a sitios relacionados con la historia de las matemáticas y también he agregado algunas referencias.

Breve Tabla Cronológica de la Historia de las Matemáticas by Juancarlos Ponce


Importante: Si has descargado este documento y encuentras algún vínculo que no funciona, por favor envíame un mail para corregirlo.

Historia de las matemáticas mexicanas

Para quienes estén interesados en conocer algo de la historia de las personas que han realizado contribuciones a las matemáticas en México, les recomiendo el siguiente sitio:
Historia de las matemáticas en México


También contiene biografías, semblanzas, anécdotas y ensayos de la historia de las matemáticas desarrolladas en Mexico. Este sitio está auspiciado por el Instituto de Matemáticas de la UNAM.