Question

2. The design of the Trieste was based on the design of a hot air balloon built by Auguste Piccard, Jacques's father. In 1932, Auguste rode in his hot-air balloon up to a record-breaking height.A. Auguste's ascent took 7 hours and went up 51,683 feet. Write a relationship y = kx to represent his ascent from his starting location.B. Auguste's descent took 3 hours and went down 52,940 feet. Write another relationship to represent his descent. C. Did Auguste Piccard end up at a greater or lesser altitude than his starting point? How much higher or lower?

Answer 1

A. y = 7383.3x

B. y = 17646.7x

C. Lesser altitude; 1257 feet

Step-by-step explanation

A. We want to write a proportional relationship between the time it took him to ascend and the total height he reached:

y = kx

where x = time taken

y = distance (height reached)

k = constant of proportionality

We have to find k for the relationship.

So, we have that:

`\begin{gathered} 51683\text{ = k }\cdot\text{ }7 \\ \Rightarrow\text{ k = }(51683)/(7) \\ k\text{ = }7383.3\text{ ft/hr} \end{gathered}`

This constant of proportionality (between distance and time) is called speed.

Therefore, the relationship for his ascent is:

y = 7383.3x

B. For his descent, we also have to find k in:

y = kx

We have that:

`\begin{gathered} 52940\text{ = k }\cdot\text{ 3} \\ k\text{ = }(52940)/(3) \\ k=\text{ }17646.7\text{ ft/hr} \end{gathered}`

Therefore, the relationship for his descent is:

y = 17646.7x

C. To find out if he reached a greater or lesser altitude than his starting point, we have to subtract his altitude during ascent from his altitude during descent.

If the value is positive then he ended up at a lesser altitude but if it is negative, he ended up on a greater altitude.

That is:

52940 - 51683

= 1257 feet

Since it is positive, that means that he descended more feet than he ascended and so, he ended up at a lesser altitude than his starting point, 1257 higher.