Question

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.

Answer 1

6.6 m/s

Step-by-step explanation:

We are given that

Length,l=14 m

`\theta=45^(\circ)`

`\theta'=30^(\circ)`

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

`v=√(2gh)`

Where
`g=9.8m/s^2`

Substitute the values

`v=√(2* 9.8* 2.22)=6.6 m/s`

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