An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The height of the first balloon decreases over time: h = 3000 − 40 m .
The height of the second balloon increases over time: h = 1200 + 50 m .
Combine the two equations to form a system of equations.
The correct system of equations representing the situation is: h = 3 , 000 − 40 m ; h = 1 , 200 + 50 m .
Explanation
Problem Analysis Let's analyze the problem. We have two hot air balloons. The first one starts at 3,000 feet and descends at 40 feet per minute. The second one starts at 1,200 feet and ascends at 50 feet per minute. We need to find the system of equations that represents their heights ( h ) after m minutes.
Equation for Balloon 1 For the first balloon, the height h decreases from its initial height of 3,000 feet by 40 feet each minute ( m ). So, the equation is: h = 3000 − 40 m
Equation for Balloon 2 For the second balloon, the height h increases from its initial height of 1,200 feet by 50 feet each minute ( m ). So, the equation is: h = 1200 + 50 m
Matching the Equations Now, let's compare our equations with the given options:
A. h = 3 , 000 − 40 m and h = 1 , 200 + 50 m B. h = 3 , 000 + 40 m and h = 1 , 200 − 50 m C. h = 3 , 000 m − 40 and h = 1 , 200 m + 50 D. m = 3 , 000 − 40 h and m = 1 , 200 + 50 h
Option A matches our derived equations.
Final Answer Therefore, the correct system of equations is: h = 3000 − 40 m h = 1200 + 50 m
Examples
Understanding how things change over time is super useful! Imagine you're tracking the water level in two tanks. One tank starts full and drains at a steady rate, while the other starts empty and fills up. Just like the balloons, you can use equations to predict the water level in each tank at any given time. This helps you manage resources, plan refills, and avoid overflows!
The current of 15.0 A for 30 seconds corresponds to a total charge of 450 coulombs. This is equivalent to approximately 2.81 billion billion electrons flowing through the device. The number of electrons can be calculated using the charge of a single electron.
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