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Alberto wants to make a scale model of the Wright​ brothers' glider. a. The wingspan of the scale model must be between 15 cm and 18 cm. What scale factor should he​ use? Explain. b. Using the scale factor from part​ a, what will be the length and height of the model​ glider? c. Assuming the wings are​ rectangles, what will be the wing area of the model​ glider? If both wing sections are the same​ size, what will be the dimensions of each wing​ section?

User Sam Jarman
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a. Alberto should use a scale factor between 0.01 and 0.012 for his scale model of the Wright brothers' glider.

b. The length and height of the model glider will be 10 cm and 2 cm, respectively.

c. The wing area of the model glider will be 1 cm^2, and each wing section will have dimensions of 1 cm by 1 cm.

a. To determine the scale factor, we need to compare the wingspan of the model glider to the actual wingspan of the Wright brothers' glider. The range given for the wingspan of the model is 15 cm to 18 cm.

Let's assume the actual wingspan of the Wright brothers' glider is 15 meters. To find the scale factor, we can use the formula:

Scale factor = Model wingspan / Actual wingspan

If we convert the actual wingspan from meters to centimeters, we get 1500 cm.

Using the lower limit of the model's wingspan (15 cm), the scale factor would be:

Scale factor = 15 cm / 1500 cm = 0.01

Using the upper limit of the model's wingspan (18 cm), the scale factor would be:

Scale factor = 18 cm / 1500 cm ≈ 0.012

So, Alberto should use a scale factor between 0.01 and 0.012 for his scale model of the Wright brothers' glider.

b. To find the length and height of the model glider, we need to apply the scale factor to the actual dimensions of the Wright brothers' glider.

Let's assume the actual length and height of the Wright brothers' glider are 10 meters and 2 meters, respectively.

Using the scale factor of 0.01 (from part a), we can find the dimensions of the model glider:

Length of model glider = Scale factor * Actual length

Length of model glider = 0.01 * 1000 cm = 10 cm

Height of model glider = Scale factor * Actual height

Height of model glider = 0.01 * 200 cm = 2 cm

Therefore, the length and height of the model glider will be 10 cm and 2 cm, respectively.

c. Assuming the wings of the glider are rectangles, we can calculate the wing area of the model glider by using the scale factor.

Let's assume the actual wing area of the Wright brothers' glider is 100 square meters.

Using the scale factor of 0.01 (from part a), we can find the wing area of the model glider:

Wing area of model glider = Scale factor^2 * Actual wing area

Wing area of model glider = 0.01^2 * 10000 cm^2 = 1 cm^2

Since both wing sections are the same size, each wing section will have a wing area of 1 cm^2.

Therefore, the wing area of the model glider will be 1 cm^2, and each wing section will have dimensions of 1 cm by 1 cm.

User EbinPaulose
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