a little spider monkey (let's call her flo) has stolen a bunch of bananas from her older brother charley and is now running away from him with the bananas in hand. she sees salvation in a long vine and grabs the bottom, hoping to swing away.

a) is flo, who has a mass of 5.3 kg, and the bananas, with a mass of 0.5 kg, reaches a height of 1.2 m before slowing down to a stop and swinging back down, how fast was she running when she grabbed the vine?

b) as she swings back down, charley (whose mass is 5.9 kg) is standing just at the bottom of the swing. he grabs her and they swing up together. what height will the two monkeys and the coveted bananas reach?

c) as a result of their fighting, they happen to drop the bananas just as the vine pendulum reaches this new height. how fast will the two monkeys be moving when they let go of the vine at the bottom again?

I got 4.8 m/s for the first answer. and 0.59 m for the second answer. Can someone please confirm these answers for me and also help me with the last question?

To determine whether your answers for parts (a) and (b) are correct, let's go through the calculations together.

(a) To find the initial speed of Flo when she grabbed the vine, we can use the principle of conservation of mechanical energy.

The potential energy gained by Flo and the bananas when they are at a height of 1.2 m is given by:

Potential energy = mass * gravity * height

Potential energy = (5.3 kg + 0.5 kg) * 9.8 m/s² * 1.2 m

Potential energy = 69.78 Joules

At the top of the swing, this potential energy is converted into kinetic energy, given by:

Kinetic energy = (1/2) * mass * velocity²

We can rearrange this equation to solve for velocity:

velocity = √(2 * Kinetic energy / mass)

Since all the potential energy is converted to kinetic energy at the top of the swing, we can substitute the potential energy value we calculated earlier for the kinetic energy:

velocity = √(2 * 69.78 J / (5.3 kg + 0.5 kg))

velocity ≈ √(2 * 69.78 J / 5.8 kg)

velocity ≈ √(2 * 12.03)

velocity ≈ √(24.06)

velocity ≈ 4.904 m/s

So, the correct answer for part (a) is approximately 4.904 m/s (rounded to three decimal places). Therefore, your answer of 4.8 m/s is close but slightly incorrect.

Now let's move on to part (b):

(b) When Charley grabs Flo as they swing back down, their combined mass becomes 5.3 kg + 0.5 kg + 5.9 kg = 11.7 kg.

The mechanical energy at the bottom of the swing is entirely converted into potential energy at the highest point of their swing.

Potential energy = mass * gravity * height

Potential energy = 11.7 kg * 9.8 m/s² * height

Given that the potential energy at the highest point of the swing will be equal to the potential energy at the previous height, we can set up the following equation:

11.7 kg * 9.8 m/s² * 1.2 m = 11.7 kg * 9.8 m/s² * height

Simplifying the equation:

1.2 m = height

So the correct answer for part (b) is 1.2 m. Therefore, your answer of 0.59 m is incorrect.

Moving on to part (c):

(c) When Flo and Charley drop the bananas, their combined mass is still 11.7 kg.

At the bottom of the swing, all their potential energy is converted into kinetic energy. We can use the same equations as in part (a) to find their velocity:

velocity = √(2 * Kinetic energy / mass)

But this time, we substitute the potential energy at the height they let go of the vine for the kinetic energy:

velocity = √(2 * Potential energy / mass)

velocity = √(2 * mass * gravity * height / mass)

velocity = √(2 * gravity * height)

velocity = √(2 * 9.8 m/s² * 1.2 m)

velocity ≈ √(2 * 11.76)

velocity ≈ √(23.52)

velocity ≈ 4.85 m/s

Therefore, the correct answer for part (c) is approximately 4.85 m/s.