Question

A weight is attached to to a spring that is fixed to the floor. The equation h=7cos (pi/3 t) models the height, h, in centimeters after t seconds of the weight being stretched and released.Solve for the solution of t and find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round to the nearest hundreth.Please help me understand how to do this problem.

Answer 1

Answer:

The times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position are 78.10s, 61.71s, and 42.41s respectively

Step-by-step explanation:

Given the equation:

`h=7\cos((\pi)/(3)t)`

Make t the subject:

`\begin{gathered} (h)/(7)=\cos((\pi)/(3)t) \\ \\ \cos^(-1)((h)/(7))=(\pi)/(3)t \\ \\ t=(3)/(\pi)\cos^(-1)((h)/(7)) \end{gathered}`

We now substitute h = 1, 3 and 5

`\begin{gathered} t=(3)/(\pi)\cos^(-1)((1)/(7))=78.10 \\ \\ t=(3)/(\pi)\cos^(-1)((3)/(7))=61.71 \\ \\ t=(3)/(\pi)\cos^(-1)((5)/(7))=42.41 \end{gathered}`

The times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position are 78.10s, 61.71s, and 42.41s respectively