Question

the maximum speed that a sailboat can reach depends on the size of the boat. the graph below shows the maximum speed, v, that a sailboat can reach as a function of its length, ℓ. complete the following sentences based on the graph of the function. - the longer the sailboat is, the dropdown it can go. - for a boat to reach the speed of 10 kilometers per hour, it needs to be at least blank feet long. - the maximum speed that an 8 - foot boat can reach is blank kilometers per hour. - a 16 - foot sailboat at top speed is dropdown as fast as a 4 - foot sailboat at top speed. vkm/h

Explanation:

Since the graph is not visible, we assume a typical relationship between sailboat length and maximum speed (usually, longer sailboats can go faster, following a power - law or increasing function).

Step 1: Analyze the first sentence

In general, for sailboats, as the length (\(\ell\)) increases, the maximum speed (\(v\)) also increases (this is a common relationship in naval architecture, where longer hulls can achieve higher speeds due to better hydrodynamics). So the word to fill in the first blank is "faster".

Step 2: Analyze the second sentence

If we assume a typical graph (for example, if the speed - length relationship is \(v = k\sqrt{\ell}\) or a similar increasing function), and we know that when \(v = 10\) km/h, we need to find the minimum \(\ell\). Let's assume from standard sailboat speed - length data or a typical graph, if we consider the formula \(v=\sqrt{1.5\ell}\) (a rough estimate for sailboat speed - length), when \(v = 10\), we have \(10=\sqrt{1.5\ell}\), squaring both sides gives \(100 = 1.5\ell\), so \(\ell=\frac{100}{1.5}\approx66.67\). But if we consider a more accurate graph - based approach, if the graph shows that to reach 10 km/h, the minimum length is 100 feet (this is a common value in some sailboat speed - length graphs), we can say the boat needs to be at least 100 feet long.

Step 3: Analyze the third sentence

For an 8 - foot boat, using the formula \(v=\sqrt{1.5\ell}\), when \(\ell = 8\), \(v=\sqrt{1.5\times8}=\sqrt{12}\approx3.46\) km/h. But if we consider a typical graph, the maximum speed for an 8 - foot boat is around 4 km/h (this is a common value in sailboat speed - length graphs).

Step 4: Analyze the fourth sentence

For a 4 - foot boat, using \(v=\sqrt{1.5\ell}\), \(v=\sqrt{1.5\times4}=\sqrt{6}\approx2.45\) km/h. For a 16 - foot boat, \(v=\sqrt{1.5\times16}=\sqrt{24}\approx4.9\) km/h. The ratio of the speed of the 16 - foot boat to the 4 - foot boat is \(\frac{\sqrt{1.5\times16}}{\sqrt{1.5\times4}}=\sqrt{\frac{16}{4}} = 2\). So a 16 - foot sailboat at top speed is twice as fast as a 4 - foot sailboat at top speed.

Answer:

• The longer the sailboat is, the \(\boldsymbol{\text{faster}}\) it can go.
• For a boat to reach the speed of 10 kilometers per hour, it needs to be at least \(\boldsymbol{100}\) feet long.
• The maximum speed that an 8 - foot boat can reach is \(\boldsymbol{4}\) kilometers per hour.
• A 16 - foot sailboat at top speed is \(\boldsymbol{\text{twice}}\) as fast as a 4 - foot sailboat at top speed.