Moderate -0.8 This is a straightforward verification question requiring substitution of coordinates into two vector line equations to find parameter values. It involves only basic algebraic manipulation and no problem-solving or geometric insight—purely routine checking that given values satisfy the equations.
From the diagram: height \(= 1\), so \(b = 1\); wavelength \(= 4\), so \(2\pi a = 4\), giving \(a = \frac{2}{\pi} \approx 0.637\)
B1
Reading off or calculating \(a\) and \(b\) from the scales
For a stable sea wave, the ratio of height to wavelength must satisfy certain conditions; here height \(= 2\) (peak to trough), wavelength \(= 4\), ratio \(= \frac{1}{2}\)
M1
Calculating the ratio \(\frac{\text{height}}{\text{wavelength}}\)
Since \(b > a\) (as \(1 > 0.637\)), or equivalently the height-to-wavelength ratio \(\frac{1}{2} > \frac{1}{7}\) (or the standard stability criterion), the wave is too steep to be a stable sea wave
A1
Valid comparison showing the curve does not satisfy the stability condition, with correct values used
# Question 5:
| Answer | Mark | Guidance |
|--------|------|----------|
| From the diagram: height $= 1$, so $b = 1$; wavelength $= 4$, so $2\pi a = 4$, giving $a = \frac{2}{\pi} \approx 0.637$ | B1 | Reading off or calculating $a$ and $b$ from the scales |
| For a stable sea wave, the ratio of height to wavelength must satisfy certain conditions; here height $= 2$ (peak to trough), wavelength $= 4$, ratio $= \frac{1}{2}$ | M1 | Calculating the ratio $\frac{\text{height}}{\text{wavelength}}$ |
| Since $b > a$ (as $1 > 0.637$), or equivalently the height-to-wavelength ratio $\frac{1}{2} > \frac{1}{7}$ (or the standard stability criterion), the wave is too steep to be a stable sea wave | A1 | Valid comparison showing the curve does not satisfy the stability condition, with correct values used |