How Can Kinetic Energy and Velocity Be Calculated at the Bottom of a Hill?

[Cali10]

(An explanation)
My physics teacher recently passed away, and had been absent due to his illness.
We had last started on acceleration, but the substitute had been working us on Kinetic, Potential energy, and Momentum.

We're having a test, and like myself, none of my classmates are ready, we've discussed this with the substitute, and the other physics teacher, whom I've already tried getting help from, is making us have this test Friday.

I literally have NO idea what I'm doing, I've looked up formulas, but I still don't understand what the heck I'm doing!

If any of you would be so great to help me, or explain how to do it, I would be so thankful!

- Cali

Homework Statement

A girl with a mass of 40 kg on a bicycle with a mass of 19 kg is at the top of a hill that is 22 m high. What is the kinetic energy of the girl and the bicycle as she arrives at the bottom of the hill?


How fast will the girl and the bicycle be going at the bottom of the hill?

Homework Equations

So I know the equation for Kinetic energy is KE = 1/2*M*V2

But I don't understand how to find it if its at the bottom of the hill?

And for the second part, I don't understand how to do it at all.

The Attempt at a Solution

I've tried, but I don't know exactly how to start it off, or anything.

 

[Delphi51]

A girl with a mass of 40 kg on a bicycle with a mass of 19 kg is at the top of a hill that is 22 m high. What is the kinetic energy of the girl and the bicycle as she arrives at the bottom of the hill?

Welcome to PF, Cali.
Start with PE at top = KE at bottom
Fill in the formula for PE, then the numbers and you can calculate the answer.

For the speed at the bottom, use
PE at top = KE at bottom
Put in the formula for KE and the number you got earlier for PE. Solve for v.

 

[tiny-tim]

Welcome to PF!

Hi Cali! Welcome to PF!

(try using the X² icon just above the Reply box )

girl with a mass of 40 kg on a bicycle with a mass of 19 kg is at the top of a hill that is 22 m high. What is the kinetic energy of the girl and the bicycle as she arrives at the bottom of the hill?

How fast will the girl and the bicycle be going at the bottom of the hill?
…
So I know the equation for Kinetic energy is KE = 1/2*M*V2

But I don't understand how to find it if its at the bottom of the hill?

You need to use conservation of energy …

KE + PE = constant, where KE = 1/2 mv² and PE = mgh (h is height),

ie KE_i + PE_i = KE_f + PE_f .

The idea is that the potential energy lost (by reducing height) is converted into increased kinetic energy (by increasing speed).

Try it! ​

 

[Cali10]

Hi Cali! Welcome to PF!

(try using the X² icon just above the Reply box )


You need to use conservation of energy …

KE + PE = constant, where KE = 1/2 mv² and PE = mgh (h is height),

ie KE_i + PE_i = KE_f + PE_f .

The idea is that the potential energy lost (by reducing height) is converted into increased kinetic energy (by increasing speed).

Try it! ​

So once I get the PE, Do I plug that into KE?
And after that I do what?

Welcome to PF, Cali.
Start with PE at top = KE at bottom
Fill in the formula for PE, then the numbers and you can calculate the answer.

For the speed at the bottom, use
PE at top = KE at bottom
Put in the formula for KE and the number you got earlier for PE. Solve for v.

Okay, so for the first part I got 12,720, and when I worked the second part I got 424.

 

[tiny-tim]

Hi Cali!

(just got up :zzz: …)

Okay, so for the first part I got 12,720

Yup!

… , and when I worked the second part I got 424.

erm … 424 metres per second on a bike??

Useful tip: always write out your formula (with m g v etc) first, and then you're less likely to make a mistake!