Wheel with radius 3 m rolls at 18 rad/s. how fast is a point on the rim of the wheel rising when the point isπ/3 radians above the horizontal and rising? round to one decimal.

The point is rising at a speed of 27 m/s.

Step-by-step explanation:

The rim is represented in the figure that is attached

The tangential speed of the point on the rim is given by

Applying values we get

Resolving the speed along the x and y axis as shown in the figure we get

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.