I need some help. I have tried working this problem and can't get it.
A scale model of the solar system is being constructed where 40cm of the model represents 0.5 AU of actual distance. What is the model dimension, in meters, for the distance of Jupiter from the sun?
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To solve this problem, let's first find out the actual distance of Jupiter from the Sun in astronomical units (AU).
The average distance between Jupiter and the Sun is approximately 5.20 AU.
Next, we need to determine the scale of the model. We are told that 40 cm of the model represents 0.5 AU.
Now, we can set up a proportion to find the model dimension in meters for the distance of Jupiter from the Sun.
40 cm x meters
------- = -------------
0.5 AU 5.20 AU
To solve for x, we can cross-multiply and divide:
(40 cm) * (5.20 AU) = (0.5 AU) * (x meters)
208 cm * AU = 0.5 * x meters
104 cm * AU = 0.5 * x meters
Now, we can convert from cm to meters:
1 meter = 100 cm
104 cm * AU = (0.5 * x meters) * (100 cm / 1 meter)
104 cm * AU = 50 * x meters
Divide both sides by 50:
(104 cm * AU) / 50 = (50 * x meters) / 50
2.08 cm * AU = x meters
Therefore, the model dimension for the distance of Jupiter from the Sun is approximately 2.08 meters.
To find the model dimension for the distance of Jupiter from the sun, we need to first understand the given scale. It states that 40cm of the model represents 0.5 Astronomical Units (AU) of actual distance.
An Astronomical Unit (AU) is the average distance between Earth and the Sun, which is approximately 149.6 million kilometers or 93 million miles.
To calculate the model dimension for the distance of Jupiter from the Sun, we can use the following steps:
1. Convert 0.5 AU to kilometers:
Since 1 AU is equal to 149.6 million kilometers, we can calculate:
0.5 AU = 0.5 * 149.6 million km = 74.8 million km
2. Convert the distance to centimeters:
Since 1 kilometer is equal to 100,000 centimeters, we can calculate:
74.8 million km = 74.8 million * 100,000 cm = 7.48 trillion cm
3. Calculate the model dimension:
Divide the distance in centimeters by the scale factor, which is 40 cm per 0.5 AU:
7.48 trillion cm / (40 cm/0.5 AU) = 7.48 trillion cm / (40/0.5) = 7.48 trillion cm / 80
Simplify the units by dividing both sides by 1 trillion (10^12) cm to get the dimension in meters:
7.48 / 80 trillion cm = 74.8 / 800 billion cm = 0.0935 trillion cm = 0.0935 million meters
Therefore, the model dimension for the distance of Jupiter from the sun is 0.0935 million meters.
Remember to always pay attention to the units and scale when doing calculations like this.