Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 14 m that makes an angle of 45∘ with the vertical, steps off his tree limb, and swings down and then up to Jane's open arms. When he arrives, his vine makes an angle of 30∘ with the vertical. Calculate Tarzan's speed just before he reaches Jane. You can ignore air resistance and the mass of the vine.

6.6 m/s

Explanation:

We are given that

Length,l=14 m

We have to find the Tarzan's speed before he reaches Jane.

Difference in height,h=Final height-Initial height=l(cos 30-cos 45)

Substitute the values

h=14(cos30-cos45)=2.22 m

Speed of Tarzan is given by

Where

Substitute the values

Hence, Tarzan's speed just before he reaches Jane=6.6 m/s

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the maxium height is 34m/s