Question

Ana and Kristoff had a romantic date in the jungle. Kristoff, in one tree, sights Ana in another tree. Trying to impress Ana, Kristoff grabs the end of a vine with a length of 20.3m that makes an angle of 45° with the vertical, steps off his tree limb, and swings down and then up to Ana's open arms. When he arrives, his vine makes an angle of 30° with the vertical. Determine whether he gives her a tender embrace or knocks her off her limb by calculating Kristoff's speed just before he reaches Ana. You can ignore air resistance and the mass of the vine.

Answer 1

$v=\sqrt{2gh(\sin 45°-\sin 30°)}=9.1~\frac ms=32.7~\frac{km}h,$

knocks her off her limb.