Tarzan, mass 85kg swings down from a tree limb on the end of a 20m vine. his feet touch the ground 4.0m below the limb.

A. how fast is Tarzan moving when he reaches the ground?

B. Does your answer depend on Tarzan's mass?

C. Does your answer depend on the length of the vine?

It doesn't even give you a proper length, it only says 4.0m below the ground, how am I supposed to know how much that is?

Need help with the overall calculations and B. And C.

(a)We know at equilibrium,

Potential energy =kinetic energy
=>m*g*h=1/2*m*v^2
=>m*g*h*2=m*v^2
=>(m*g*h*2)/m=v^2
=>2*g*h=v^2
=>sqrt(2*g*h)=v
=>v=sqrt(2*g*h)
Now putting the values,
v=sqrt(2*10*4)
=>sqrt(80)
=>8.944m/s^2 OR (after rounding off) 9m/s^2
Therefore he was moving with 9m/s^2 speed /velocity when he reached the ground. =Ans
(b) No, our answer does not depend upon his mass, because it gets cancelled in the process.
(c) No, our answer does not depend on the length of the vine either, because it is not required in the process.
Hope it helps you, if it does, just pray, that I may succeed in my boards this year with brilliant marks.. Please😊😊

The solutions were cleared

Using the kinematics formula:

v^2 = Vo^2 +2ad
Vf^2 = 2(9.80)(4.0)
Vf^2 = 78.4
V = 8.9 m/s

To calculate Tarzan's speed when he reaches the ground, we can use the principle of conservation of energy. At the start of the swing, all of Tarzan's potential energy (due to his height above the ground) is converted into kinetic energy (due to his motion).

The potential energy (PE) is given by the equation PE = mgh, where m is the mass of Tarzan (85kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height above the ground (20m - 4m = 16m since he swings down 4m below the limb).

So, the potential energy at the start is PE = (85kg)(9.8m/s^2)(16m) = 13,328 J.

At the bottom of the swing, all of the potential energy is converted into kinetic energy (KE). The kinetic energy is given by the equation KE = (1/2)mv^2, where v is Tarzan's speed.

Setting the potential energy equal to the kinetic energy, we have:

PE = KE
13,328 J = (1/2)(85kg)v^2

Rearranging the equation, we find:

v^2 = (2 * 13,328 J) / 85kg
v^2 = 313.1 m^2/s^2

Taking the square root of both sides, we get:

v = √(313.1 m^2/s^2) ≈ 17.7 m/s

So Tarzan's speed when he reaches the ground is approximately 17.7 m/s.

Now let's consider the other questions:

B. Does your answer depend on Tarzan's mass?
No, the speed does not depend on Tarzan's mass. The mass cancels out in the calculation, so the result is the same regardless of Tarzan's mass. This means that Tarzan's speed would be the same, even if his mass were different.

C. Does your answer depend on the length of the vine?
No, the speed does not depend on the length of the vine either. The only factor that influences the speed is the height from which Tarzan swings. The vine's length is not relevant in calculating Tarzan's speed.

Strictly speaking, his speed at the bottom would not depend upon where his feet are, it would depend upon how far his center of mass dropped. You also need to know where he gripped the vine. Maybe he did not hold it at the very end.

They also do not say if the vine was initially horizontal. This information is also needed.

They probably expect you to assume
V(bottom)^2/2 = g (20 + 4 meters)

It is not a well defined problem