Question

It is known that the vertical component of velocity for a particular roller coaster is modelled by the following function: v(t) = 65 cos (2t), where v(t) is in m/s and (t) is in seconds. The height of the roller coaster cannot exceed 60 metres high due to council safety regulations. It is known that at time t = 2 s, the height of the roller coaster is 24.5 metres. Will the roller coaster be passed as safe by the council? You must show all necessary mathematical working to support your answer. Assume angles are in radians.

Answer 1

So, the highest point of cosine occurs at 2pi radians or 180degrees
and cos(180)=1
this tells you that at t=180 or 2pi the height of the roller coaster must be
v(t)=65(1) = 65 and exceeds the regulation (and will every 180,360,720, etc)

Okay, so the t=2s is 24.5 meters is just insane and not ture.
65*cos(2*2)
65cos(4)
-42.48 rad

I postponed this post and then converted to degrees after I saw that, but in both rad and degrees that is not true... so whatever, just say its 2pi,4pi etc. no matter what it goes to 65 as its max in rad and deg

Answer 2

Thank You