Further maths Core Pure Edexcel June 2019 Question 5(b):
$5. $ An engineer is investigating the motion of a sprung diving board at a swimming pool. Let $E$ be the position of the end of the diving board when it is at rest in its equilibrium position and when there is no diver standing on the diving board.
A diver jumps from the diving board.
The vertical displacement, $h$ cm, of the end of the diving board above $E$ is modelled by the differential equation
$$ 4\frac{d^2 h}{dt^2} + 4\frac{d h}{dt} + 37 h = 0 $$
Where $t$ seconds is the time after the diver jumps.
$(a)$ Find a general solution of the differential equation.
When $t=0$, the end of the diving board is $20\,\mathrm{cm}$ below $E$ and is moving upwards with a speed of $55$ $\mathrm{cm}\,s^{–1}$.
$(b)$ Find, according to the model, the maximum vertical displacement of the end of the diving board above $E$.
You can find the mark scheme here.
And a model answer to the question here.
In the model answer to $(b)$, they wrote, "answer is negative as it is the displacement above $E$ (which is negative). Remember: displacement is a vector. "
I think this is incorrect because based on the definition of displacement in the question, the displacement of the diving board above $E$ is $(+)16.7\,\mathrm{cm}$, not $-16.7\,\mathrm{cm}$. Am I right or wrong? If wrong, then why?