When will the velocity vector make an angle of 45 degrees?

In summary, the conversation discusses finding the point at which the velocity vector of a given vector r will make an angle of 45 degrees. The individual has taken the derivative of r to find the velocity vector, but is unsure of how to proceed. A hint is given to consider the ratio of V_y to V_x when the angle is 45 degrees, which is 1 due to the equal values of sin and cos.
  • #1
bharp24
15
0
i have been given that vector r = bt^2i + ct^3j where b and c are positive constants, and i need to know when the velocity vector will make an angle of 45 degrees.

i have been trying to figure it out and am just confused. i have taken the derivative of vec r, because i know that it becomes velocity but i don't know what to do from there. i cannot figure out the components of what makes up the velocity vector. i feel like i am going in circles. please someone help!
 
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  • #2
Hint: When the velocity vector makes an angle of 45 degrees with respect to the horizontal, what can you say about [itex]V_y/V_x[/itex]?
 
  • #3
it will = 1 because the sin and cos of 45 degrees are the same...right?
 
  • #4
Right!
 

Related to When will the velocity vector make an angle of 45 degrees?

1. What is a velocity vector?

A velocity vector is a representation of the speed and direction of an object's motion. It includes both a magnitude (the speed) and a direction, and is typically represented by an arrow pointing in the direction of motion.

2. How is a velocity vector different from a regular vector?

A velocity vector is a specific type of vector that represents an object's motion, while a regular vector can represent any quantity with both magnitude and direction. Velocity vectors are typically used in physics and engineering to analyze the motion of objects.

3. How do you calculate the magnitude of a velocity vector?

The magnitude of a velocity vector can be calculated by taking the square root of the sum of the squares of its components. In other words, it is the length of the arrow representing the vector.

4. Can a velocity vector change over time?

Yes, a velocity vector can change over time if the object's speed or direction of motion changes. This is known as acceleration, and it is represented by a change in the velocity vector's magnitude or direction.

5. How is a velocity vector useful in understanding motion?

A velocity vector is useful in understanding motion because it provides a visual representation of an object's speed and direction of motion. By analyzing changes in the velocity vector over time, we can gain insights into an object's acceleration, trajectory, and other important aspects of its motion.

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