# How Do You Calculate the Velocity Vector When a Particle's Position is x=25?

• leunglik
In summary, a particle is moving in the xy-plane with its position given by x(t)=5t+3sint and y(t)=(8-t)(1-cost). The velocity vector at the time when the particle's horizontal position is x=25 is (7.008, -2.228). To find this, you need to solve the equation 5t+ 2sin(t)= 25 numerically using a bisection method or a graphing calculator.
leunglik
A particle moves in the xy-plane so that the position of the particle is given by
x(t)=5t+3sint , y(t)=(8-t)(1-cost)

Find the velocity vector at the time when the particle's horizontal position is x=25

*the x=25, i think the trick is somehow get the t with that..

Yes, it is. You have to solve 5t+ 2sin(t)= 25. There is no "algebraic" way to solve an equation like that. You will have to do it numerically. If you have a graphing calculator, you could see where the graphs of y= 5t+ 2sin(t) crosses the graph of y= 25.

If not, you might use a "bisection" method. For example, It is obvious that X(4)= 20+ 3sin(4)< 25. It is not so obvious but easy to show with a calculator that X(7)= 28+ 3 sin(7)> 25 (but not 5 or 6). The function must be equal to 25 some place between them. Just because it is simplest, try half way between them, 5.5. X(5.5)= 25.3> 25. Now we know the function is equal to 25 some place between 4 and 5.5. Again, try half way: (4+ 5.5)/2= 4.75. X(4.75)= 20.817< 25 so now we know the solution is somewhere between 4.75 and 5.5. Half way between them is (4.75+ 5.5)/2= 5.125.

Continue unfil you feel you have sufficient accuracy.

## 1. What is a vector problem?

A vector problem is a mathematical problem that involves the use of vectors, which are quantities that have both magnitude and direction. Vectors are often represented by arrows in diagrams and can be added, subtracted, and multiplied to solve a problem.

## 2. What are some real-life examples of vector problems?

Some real-life examples of vector problems include calculating the force and direction of a moving object, determining the velocity and direction of a moving vehicle, and finding the displacement and direction of a hiker's journey.

## 3. How do you solve a vector problem?

To solve a vector problem, you first need to identify the given vectors and their directions. Then, use the appropriate vector operations (addition, subtraction, and multiplication) to find the resultant vector. Finally, use trigonometric functions to find the magnitude and direction of the resultant vector.

## 4. What is the importance of vector problems in science?

Vector problems are essential in science because they allow us to describe and analyze quantities that have both magnitude and direction, such as force, velocity, and acceleration. These concepts are crucial in understanding and predicting the behavior of objects and systems in the physical world.

## 5. How can I improve my skills in solving vector problems?

The best way to improve your skills in solving vector problems is through practice. Start with simple examples and gradually move on to more complex ones. Also, make sure to understand the basic principles and operations involved in solving vector problems. You can also seek help from textbooks, online tutorials, and practice problems to enhance your skills.

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