How can you accurately hit a trash bin while biking with an apple core?

[RUber]

Va is a relative velocity. http://www.physicstutorials.org/home/mechanics/1d-kinematics/relative-motion

Thank you for clarifying.
In any case, you did not add your vectors properly.
Va + Vb = Vi, right? And Vi has vertical, right, and forward components. Vb only has a forward component.
So Va will have the same vertical and right component as Vi. Va's forward component will be Vi(forward) - Vb.

 

[RUber]

I just do not get why is there portions moving to the left, as you say...

Edited, that was moving to the right in the diagram.

 

[kongen]

What is Va? Are you still subtracting the velocity of the bike directly from the velocity of the apple? How can the speed you calculated at the end be more than the speed you started with of 8.73? That is not right.

First, break the initial velocity into its components.

8.731 * sin(20) is your vertical component
8.731 * cos(20) is your flat component.
3/5 ( 8.731 * cos(20) ) is the portion of the flat component moving to the *edit* right.
4/5 ( 8.731 * cos(20) ) is the portion of the flat component moving forward.

Then, and only then, can you subtract the velocity of the bike. And, you only subtract the velocity of the bike from the component pointing in the same direction as the bike.
Once you have done that, you have your answer...in vector component form.

If you want to see the speed, then take sqrt ( [8.731 * sin(20)]^2 + [3/5 ( 8.731 * cos(20) ) ]^2 + [ 4/5 ( 8.731 * cos(20) ) - Vbike ] ^2 ).
That is the speed in the direction of the throw.

where do you get the angle 20 from?

 

[coffeemanja]

Thank you for clarifying.
In any case, you did not add your vectors properly.
Va + Vb = Vi, right? And Vi has vertical, right, and forward components. Vb only has a forward component.
So Va will have the same vertical and right component as Vi. Va's forward component will be Vi(forward) - Vb.

Yes, if you look at the diagram as at is in the problem...origin is the bike, x to the right, y -up. The Vi forward component is equal 8,73...no?

 

[coffeemanja]

If we look at the situation as flat diagram, vi(flying apple) is 8,73. Vb is 5,6. Given that relative velocity = v object (Apple)-v observer(me on the bike). I find angles irrelative.

 

[RUber]

Yes, if you look at the diagram as at is in the problem...origin is the bike, x to the right, y -up. The Vi forward component is equal 8,73...no?

No. 8.73m/sec was the total magnitude of the initial velocity. Each component, accordingly would be less than that.

 

[RUber]

If we look at the situation as flat diagram, vi(flying apple) is 8,73. Vb is 5,6. Given that relative velocity = v object (Apple)-v observer(me on the bike). I find angles irrelative.

Without angles, how do you properly add the vectors?

The bike is not traveling in the same direction as the apple, so subtraction of magnitudes does not work.

 

[coffeemanja]

Without angles, how do you properly add the vectors?

The bike is not traveling in the same direction as the apple, so subtraction of magnitudes does not work.

For Vi= xi+yj

 

[coffeemanja]

For Vi= xi+yj

Vi=Vxi+Vyi

 

[RUber]

Vi=Vxi+Vyi

What about Vzi?

 

[coffeemanja]

What about Vzi?

I am looking at situation schematicly(flat). All vectors then have only two components.

 

[coffeemanja]

If I'm on the bike, I do not see the Vzi. Apple just moves away. I do not know what to do anymore.

 

[RUber]

Okay. Then you need to flatten the initial velocity vector, which has 3 dimensions. You can do this by multiplying by the cosine of the elevation angle.

 

[coffeemanja]

Okay. Then you need to flatten the initial velocity vector, which has 3 dimensions. You can do this by multiplying by the cosine of the elevation angle.

Then I get 8,2. 8,2-5,6=2,6 is then relative velocity.

 

[RUber]

No. The bike is not moving in the direction of the trash can.
The bike is moving forward.
The forward velocity is 4/5 of the flat velocity.

 

[coffeemanja]

No. The bike is not moving in the direction of the trash can.
The bike is moving forward.
The forward velocity is 4/5 of the flat velocity.

I will look at it tomorrow with fresh eyes. Do not want to bother you anymore here. Thank you.

 

[coffeemanja]

No. The bike is not moving in the direction of the trash can.
The bike is moving forward.
The forward velocity is 4/5 of the flat velocity.

RUber, be proud. You are great! I got it, was too tired to understand.

 

[RUber]

RUber, be proud. You are great! I got it, was too tired to understand.

Thanks. Glad it made more sense after some sleep.