Question

Tarzan wishes to use a light vine to swing from the ground onto a tree branch 3.5m high. How fast should he be going when he grabs the vine?

Answer 1

According to the energy conservation, Tarzan's initial kinetic energy should be equal to his final potential energy:

$$K = U\\ \dfrac{mv^2}{2} = mgh$$

where $m$ is his mass, $v$ is his speed, $g = 9.8m/s^2$ is the gravitational acceleration, and $h = 3.5m$ is his final height. Thus, expressing initial velocity, obtain:

$$v = \sqrt{2gh}\\ v = \sqrt{2\cdot9.8\cdot 3.5 } \approx 8.3m/s$$

Answer. 8.3 m/s.