question 13 (1 point) meghan sets up her model train on a circular track that is 1 metre wide and that sits…

question 13 (1 point) meghan sets up her model train on a circular track that is 1 metre wide and that sits in her bedroom doorway, half in her bedroom and half in the hallway. each round trip takes 2 seconds, and the train starts as far into the bedroom as possible. how deep into her bedroom the train engine is in terms of time is modelled by which equation? a) d(s)=0.5cos(180s)° b) d(s)=cos(360s)° c) d(s)=0.5cos(360s)° d) d(s)=cos(180s)°

question 13 (1 point) meghan sets up her model train on a circular track that is 1 metre wide and that sits in her bedroom doorway, half in her bedroom and half in the hallway. each round trip takes 2 seconds, and the train starts as far into the bedroom as possible. how deep into her bedroom the train engine is in terms of time is modelled by which equation? a) d(s)=0.5cos(180s)° b) d(s)=cos(360s)° c) d(s)=0.5cos(360s)° d) d(s)=cos(180s)°

Answer

Explanation:

Step1: Recall the general form of a cosine - function for periodic motion

The general form of a cosine - function for periodic motion is $d(s)=A\cos(Bs)$, where $A$ is the amplitude and $B$ is related to the period $T$ by $T=\frac{360^{\circ}}{B}$.

Step2: Determine the amplitude

The track is 1 metre wide. The train moves from one extreme to the other. The maximum displacement (amplitude) from the mid - point (the doorway) is half of the width of the track. So, $A = 0.5$ since the width of the track is 1 metre.

Step3: Determine the value of $B$

The period $T$ of the train's motion (a round - trip) is 2 seconds. We know that $T=\frac{360^{\circ}}{B}$. Substituting $T = 2$ into the formula, we get $2=\frac{360^{\circ}}{B}$, then $B = 180^{\circ}$.

Step4: Write the function

The function that models the depth $d$ of the train engine into the bedroom as a function of time $s$ is $d(s)=0.5\cos(180s)^{\circ}$.

Answer:

a) $d(s)=0.5\cos(180s)^{\circ}$