Calculating Kinetic Energy for an Object at an Angle

[Alameen Damer]

I have a question regarding how to calculate kinetic energy. Let's say I was to find the kinetic energy of a ball shot at 180 m/s at a 45 degree angle. Do i simply sub in 180 as v (velocity) in the kinetic energy equation (1/2mv^2) or must it be split into components?

 

[Bystander]

Is energy a scalar or a vector quantity?

 

[Alameen Damer]

Scalar

 

[Alameen Damer]

My textbook gives me a question that reads: A baseball is thrown from a cliff of 41m at at a velocity of 22 m.s/ The ball is thrown at at 37 degree angle. What's the ball's velocity before hitting the ground?

Why do they give this angle if it has no use in this question? I know how to get the answer, but is there a time that the angle must be used?

 

[Bystander]

What's the ball's velocity

Is velocity a scalar or a vector?

 

[Alameen Damer]

Velocity is a vector, but how does the angle play a part in it-why don't they just say it is shot at 22m/s horizontally, there is no use of the angle is there?

 

[Bystander]

It doesn't say, "horizontally." What you've given isn't clear; the 37 degrees could be a compass heading, elevation above horizontal, declination below vertical.

 

[Alameen Damer]

Sorry, it is elevation above the horizontal

 

[Bystander]

And you need to look at the horizontal and vertical components for velocities, and time of flight.

 

[Alameen Damer]

Ok so i did some calculations, calculating the kinetic energy in x(22cos37) and y(22sin37) components and adding them together equals the kinetic energy when calculated from the angled velocity (22 m/s). So basically my question is, is there a reason I should calculate the kinetic energy in components as opposed to the complete vector for a problem like this?

 

[Bystander]

a reason I should calculate the kinetic energy in components

No. 22² = 484 = (1+1+1+1+1+1+1+1+1+1 + 1+1+1+1+1+1+1+1+1+1 + 1+1)².

 

[Doc Al]

Ok so i did some calculations, calculating the kinetic energy in x(22cos37) and y(22sin37) components and adding them together equals the kinetic energy

Realize that $\sin^2\theta + \cos^2\theta = 1$.

 

[sophiecentaur]

My textbook gives me a question that reads: A baseball is thrown from a cliff of 41m at at a velocity of 22 m.s/ The ball is thrown at at 37 degree angle. What's the ball's velocity before hitting the ground?

Why do they give this angle if it has no use in this question? I know how to get the answer, but is there a time that the angle must be used?

You have a textbook. The questions in textbooks are usually based on what the book discusses. Have you looked in the book to find out about trajectories? You could also look on this Hyperphysics Link which tells you the necessary stuff in a condensed way. If you approach this algebraically (using the formulae and symbols, instead of putting figures in, you could obtain an answer that would (or would not) contain the angle - so you could answer your own question.

 

[Doc Al]

Why do they give this angle if it has no use in this question?

Note that they ask for the velocity, not simply the kinetic energy.

Of course, if all they want is the magnitude of the velocity, then perhaps you do not need the angle. That's for you to realize. There are many ways to skin a cat.

 

[russ_watters]

Why are you using kinetic energy at all for this problem? As sophiecentaur said, you have a book: what method do they use in the sample problems?

 

[Alameen Damer]

My book doesn't provide a method for a question like this, just the answer-which is given to me as 36 m/s. So I am having trouble understanding how to/if i should implement direction as they haven't given one in the answer.

 

[Doc Al]

My book doesn't provide a method for a question like this, just the answer-which is given to me as 36 m/s. So I am having trouble understanding how to/if i should implement direction as they haven't given one in the answer.

What is the topic of the book chapter where this question was asked? Is it a chapter on energy conservation? Or on projectile motion?

You certainly do not need to use the angle to find the final speed. If you've covered both energy methods and projectile motion, they solve it both ways.

 

[Alameen Damer]

Yes it is a unit on conservation of energy, momentum etc.

 

[Doc Al]

Yes it is a unit on conservation of energy, momentum etc.

Then why not use energy methods? (The purpose of giving the angle is to make you think! Does the answer depend on the angle?)

 

[Alameen Damer]

So there is no use of the direction for the final velocity as they only ask for speed-my question still stands though, why did they give us an angle, is it ideal to be solved in terms of components?

 

[Doc Al]

So there is no use of the direction for the final velocity as they only ask for speed-my question still stands though, why did they give us an angle, is it ideal to be solved in terms of components?

They gave the angle to make you think! Well then... think!

Does the angle make a difference?

 

[Alameen Damer]

Yes, so the method I did was to calculate the initial potential energy, as well as the kinetic energy, add them to get the mechanical energy. Then I would sub in this value in as kinetic energy alone, as before hitting the ground it would be all converted to kinetic energy. The angle does NOT make a difference in this particular question, however is there an example of a question where it would make a difference, and thus solving in components would be ideal?

 

[russ_watters]

I guess an energy method is implied then...

How does the speed of the object change during its flight? What makes it change? Can you think of how that relates to energy?
[Edit] looks like you got most of that.

 

[Alameen Damer]

The conversion of potential energy to kinetic energy, assuming it is in a closed system with no outside forces.

 

[Doc Al]

The angle does NOT make a difference in this particular question,

Good!

however is there an example of a question where it would make a difference, and thus solving in components would be ideal?

Sure. What if they asked: What angle does the object's velocity make when it hits the ground? Or: How high does the object rise before falling?

 

[Alameen Damer]

I see, yes that would change the scenario.

In a case like that, would I need to add up the mechanical energy for the x component, and the y component, separately, then sub each into the kinetic energy equation to find the velocity in each component, then use trig to find the angle?

 

[Doc Al]

In a case like that, would I need to add up the mechanical energy for the x component, and the y component, separately, then sub each into the kinetic energy equation to find the velocity in each component, then use trig to find the angle?

I would use standard projectile motion methods. Have you studied those? (Those are typically covered before getting to energy methods. They involve kinematics.)

 

[Alameen Damer]

Oh okay, and yes I know them. Thank you very much for the help!