Weather Balloons. Weather balloons are used to gather temperature and pressure data at var...

Weather Balloons. Weather balloons are used to gather temperature and pressure data at various altitudes in the atmosphere. The balloon rises because the density of the helium inside the balloon is less than the density of the surrounding air outside the balloon. As the balloon rises, the surrounding air becomes less dense, and thus the balloon’s ascent slows until it reaches a point of equilibrium. During the day, sunlight warms the helium trapped inside the balloon, which causes the helium to expand and become less dense; thus, the balloon will rise higher. During the night, however, the helium in the balloon cools and becomes more dense; thus, the balloon will descend to a lower altitude. The next day, the sun heats the helium again and the balloon rises. Over time, this process generates a set of altitude measurements that can be approximated with a polynomial equation. Assume that the following polynomial represents the altitude or height in meters during the first 48 hours following the launch of a weather balloon:

Alt(t) = –0.12t4 + 12t3 – 380t2 + 4100t + 220,

where the units of t are hours. The corresponding polynomial model for the velocity in meters per hour of the weather balloon is

v(t) = –0.48t3 + 36t2 – 760t + 4100.

Figure contains a plot of the altitude and velocity of the balloon for a period of 48 hours. From the plots, we can see the periods during which the balloon rises or falls.

Figure Velocity and altitude data for a weather balloon.

Modify the program in Problem so that it will check to be sure that the final time is greater than the initial time. If it is not, ask the user to reenter the complete set of report information.

Problem

Weather Balloons. Weather balloons are used to gather temperature and pressure data at various altitudes in the atmosphere. The balloon rises because the density of the helium inside the balloon is less than the density of the surrounding air outside the balloon. As the balloon rises, the surrounding air becomes less dense, and thus the balloon’s ascent slows until it reaches a point of equilibrium. During the day, sunlight warms the helium trapped inside the balloon, which causes the helium to expand and become less dense; thus, the balloon will rise higher. During the night, however, the helium in the balloon cools and becomes more dense; thus, the balloon will descend to a lower altitude. The next day, the sun heats the helium again and the balloon rises. Over time, this process generates a set of altitude measurements that can be approximated with a polynomial equation. Assume that the following polynomial represents the altitude or height in meters during the first 48 hours following the launch of a weather balloon:

Alt(t) = –0.12t4 + 12t3 – 380t2 + 4100t + 220,

where the units of t are hours. The corresponding polynomial model for the velocity in meters per hour of the weather balloon is

v(t) = –0.48t3 + 36t2 – 760t + 4100.

Figure contains a plot of the altitude and velocity of the balloon for a period of 48 hours. From the plots, we can see the periods during which the balloon rises or falls.

Figure Velocity and altitude data for a weather balloon.

Write a program that will print a table of the altitude and the velocity for this weather balloon using units of meters and meters per second. Let the user enter the start time, the increment in time between lines of the table, and the ending time, where all the time values must be less than 48 hours. Use the program to generate a table showing the weather balloon information every 10 minutes over a 2-hour period, starting 4 hours after the balloon was launched.