Question

3. A 92 kg Tarzan is holding on to a level 22m vine. He swings on the vine. What will his speed at the bottom of the swing be?

Please help A.S.A.P.!!!!!

Answer 1

Tarzan's speed at the bottom of the swing can be found using the conservation of energy principle, resulting in approximately 20.76 m/s.

Step-by-step explanation:

To find Tarzan's speed at the bottom of the swing, we use the principle of conservation of energy. Initially, Tarzan has gravitational potential energy (GPE) when the vine is level. As he swings down, this potential energy is converted into kinetic energy (KE).

At the bottom of the swing, assuming no energy loss to friction or air resistance, all GPE has been converted into KE. The formula for potential energy is U = mgh, where m is mass, g is the acceleration due to gravity, and h is height. The formula for kinetic energy is KE = ½mv², where v is velocity. Setting GPE equal to KE and solving for v gives v = √(2gh).

Substituting the known values, g = 9.8 m/s² and h = 22 m, we get:

v = √(2 × 9.8 m/s² × 22 m) = √(431.2 m²/s²) ≈ 20.76 m/s.

Therefore, Tarzan's speed at the bottom of the swing would be approximately 20.76 m/s.

Answer 2

To solve this problem, we must always remember that energy is conserved. In this case, since he is falling down, he has highest potential energy at the top and zero at bottom. While his kinetic energy is zero at the top since he started from rest and highest at the bottom. We can also say that Potential Energy lost is Kinetic Energy gained thus,

- ΔPE = ΔKE ---> one is negative since PE is losing energy

- m g (h2 – h1) = 0.5 m (v2^2 – v1^2)

Where,

m = mass of tarzan (cancel that out)

g = gravitational acceleration

h2 = height at the bottom= 0

h1 = height at top = 22 m

v2 = velocity at the bottom

v1 = velocity at top = 0 (started from rest)

Therefore substituting all values:

- 9.8 (- 22) = 0.5 (v2^2)

v2 = 20.77 m / s (ANSWER)