a. To solve the equation for t, we need to isolate t.
h = 7 cos (Et)
Divide both sides by 7:
h/7 = cos (Et)
Inverse cosine both sides:
cos^(-1) (h/7) = Et
t = cos^(-1) (h/7) / E
b. To find the times at which the weight is first at a height of 1 cm, 3 cm, and 5 cm above the rest position, we substitute each height value into the equation and solve for t.
For h = 1 cm:
t = cos^(-1) (1/7) / E = 0.813 / E
For h = 3 cm:
t = cos^(-1) (3/7) / E = 1.231 / E
For h = 5 cm:
t = cos^(-1) (5/7) / E = 1.375 / E
Therefore, the weight is first at a height of 1 cm above the rest position at approximately 0.81 / E seconds, at a height of 3 cm above the rest position at approximately 1.23 / E seconds, and at a height of 5 cm above the rest position at approximately 1.38 / E seconds.
A weight is attached to a spring that is fixed to the floor. The
equation h = 7 cos (Et)
models the height, h, in centimeters after t seconds of the weight being stretched and released.
a. Solve the equation for t.
b. 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.
Calculate your answer using radian angle measure. Round your answers to the nearest hundredth.
1 answer