Question

Tarzan (mT=85.0 kg) is perched on a cliff 16.0 m above Jane. Jane is in the foreground is looking forwards. In the background, Tarzan has jumped off of a cliff and is swinging on a vine towards Jane. A red curved arrow points from Tarzan to Jane, showing the path he will swing on. Answer the three questions below, using three significant figures. Part A: What is the value of Tarzan's speed (vT) just as he gets down to Jane's level?

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

Part A

The velocity of Tarzan is
`v_T = 17.7 \ m/s`

Part B

The percentage loss of kinetic energy is %-loss
`= 61.4`%

Part C

The speed would be exactly the same

Step-by-step explanation:

From the question we are told that

The mass of Tarzan is
`m = 85.5 \ kg`

The height of the cliff is
`h = 16.0 \ m`

From the law of conservation of energy

`PE = KE`

Where PE is the potential energy of Tarzan at the top of the cliff which is mathematically represented as

`PE = mgh`

KE is the kinetic energy of Tarzan as he swings toward jane and is mathematically represented as

`KE = (1)/(2) mv^2_T`

So

`mgh = (1)/(2)m v_T^2`

=>
`gh = (1)/(2) v_T^2`

Substituting values

`9.8 * 16 = (1)/(2) v_T^2`

=>
`v_T = \sqrt{(9.8 * 16)/(0.5) }`

`v_T = 17.7 \ m/s`

From the question we are told that the actual velocity of Tarzan is

`v = 11 m/s`

The kinetic energy at the the velocity is mathematically represented as

`KE_A = (1)/(2) m v^2`

Substituting values

`KE_A = (1)/(2) (85) * 11^2`

`KE_A = 5142.5 J`

The kinetic energy at
`v_T` is

`KE = (1)/(2) * 85 * 17.7^2`

=>
`KE = 13314.83\ J`

Now the percentage loss of kinetic energy is mathematically evaluated as

%-loss
`= (KE - KE_A)/(KE) * 100`

substituting values

%-loss
`= (13314.83 - 5142.5)/(13314.83) * 100`

%-loss
`= 61.4`%

The mass of Tarzan does not affect the speed because looking at this equation

`gh = (1)/(2) v_T^2`

We see that the velocity of Tarzan is not dependent on the mass of Tarzan