Trajectory

Nelka holds a dumbbell in her hand at arm's length. Then she lifts it by bending her arm only at the elbow, making an angle of 135°. The exercise ends with the dumbbell lowering along the same path. What is the length of the trajectory the dumbbell follows if Nelka repeats the exercise 15 times with each hand and her forearm is 30cm long?

Final Answer:

s =  29.3618 m

Step-by-step explanation:

$$\begin{gathered} r=30\text{cm}\to \text{m}=30:100\text{m}=0.3\text{m} \\ \alpha =135{}^{\circ } \\ n=2\cdot 15=30 \\ o=2\pi \cdot r=2\cdot 3.1416\cdot 0.3\doteq 1.885\text{m} \\ k=\frac{\alpha }{260}=\frac{135}{260}=\frac{27}{52}\doteq 0.5192 \\ s=o\cdot k\cdot n=1.885\cdot 0.5192\cdot 30=29.3618\text{m} \end{gathered}$$

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