Velocity of a bee moving along the curve of intersection of 2 surfaces

In summary, the person is having trouble understanding how to determine whether f2(x,y,z) should be x2-y2-z or z-x2+y2. They mention that the bee is moving in the increasing direction of z, but are unsure of how this relates to the function. They also question if both answers could be acceptable. However, they later state that they have figured it out themselves.
  • #1
karokr94
10
0
Hi, I've attached the problem and the solution. I understand the solution except for one thing. I've circled the part I'm having problems with. How do I decide if the circled part should be
f2(x,y,z)=x2-y2-z or
f2(x,y,z)=z-x2+y2

I'm sure it has something to do with the fact that the problem statement states that the bee is moving in the increasing direction of z, but I just can't figure out how it translates into f2 being one or the other. Or are both answers acceptable?

Thanks in advance for the help!
 

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  • #2
Never mind, I figured it out.
 

Related to Velocity of a bee moving along the curve of intersection of 2 surfaces

1. What is the velocity of a bee moving along the curve of intersection of 2 surfaces?

The velocity of a bee moving along the curve of intersection of 2 surfaces refers to the speed and direction at which the bee is moving at a specific point on the curve. It is a vector quantity that takes into account both the magnitude (speed) and direction of the bee's movement.

2. How is the velocity of a bee calculated along the curve of intersection of 2 surfaces?

The velocity of a bee along the curve of intersection can be calculated by taking the derivative of the position vector with respect to time. This will give us the instantaneous velocity at a specific point on the curve. Alternatively, we can also use the formula v = d/t, where v is the velocity, d is the distance traveled, and t is the time taken.

3. Can the velocity of a bee change along the curve of intersection of 2 surfaces?

Yes, the velocity of a bee can change along the curve of intersection. This is because the bee may be accelerating or decelerating, changing its speed and direction as it moves along the curve. The velocity of the bee will be constantly changing unless it is moving at a constant speed in a straight line.

4. How does the shape of the curve affect the velocity of the bee?

The shape of the curve can have a significant impact on the velocity of the bee. If the curve is smooth and gradual, the bee's velocity will remain relatively constant. However, if the curve is sharp or has sudden changes in direction, the bee's velocity may change abruptly. This is because the bee will have to accelerate or decelerate to follow the curve.

5. Is the velocity of a bee along the curve of intersection affected by the surfaces it is moving on?

Yes, the velocity of a bee along the curve of intersection can be affected by the surfaces it is moving on. For example, if the bee is moving along a curve where one surface is rough and the other is smooth, the bee's velocity may change as it moves from one surface to the other. This is because the friction between the bee and the surfaces will affect its speed and direction.

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