Vector velocity homework question

In summary, John has a position vector of 40j metres and wants to skate to the point with a position vector of 30i metres. With a constant speed of 5ms^-1, his velocity can be found by dividing the magnitude of the velocity vector by the magnitude of the resultant position vector. The difference between the final and initial position vectors, which is -30i + 40j, gives the direction of the velocity vector.
  • #1
Gughanath
118
0
On an occasion, John has position vector 40j metres. He wished to skate in a straightline to the point with position vector 30i metres. Given that his speed is constant at 5ms^-1, find his velocity.
Someone help me on this one please! :confused:
 
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  • #2
You have a magnitude (5 meters per second).

The starting coordinates (0,40) and the ending coordinates (30,0) supply the direction. Relative to your origin (0,0) your two position vectors are 0i + 40j and 30i + 0j

Since you're using ijk coordinates, your best bet is to add your two position vectors together. Then you have a scalar problem: x(30i + 40j) = v

To find x, you have to divide the magnitude of the velocity vector by the magnitude of the resultant position vector. Plug the coordinates of your position vector into the Pythagorean Theorem.

Once you determine x, do the scalar mutliplication (multiply each of the resultant position vector coordinates by x).
 
  • #3
Oh!...Thanx
 
  • #4
Gughanath said:
Oh!...Thanx

You need the difference between the final and initial position vectors, not their sum, to get the direction of your velocity vector

[tex]
\overrightarrow {\Delta r} = \overrightarrow{r}_{final} - \overrightarrow {r}_{initial} = 30\widehat{i} - 40\widehat{j}
[/tex]

Since you know the magnitude of your velocity vector, you need to find the unit vector in the direction of [tex]\overrightarrow {\Delta r} [/tex]. You can do that by dividing the vector [tex] \overrightarrow {\Delta r} [/tex] by its length. Then multiply that unit vector by the magnitude of the velocity you have.
 
  • #5
Oops. OlderDan's right. It's final position minus start position.

It's -30i +40j , not +30i.
 

Related to Vector velocity homework question

1. What is vector velocity?

Vector velocity is a mathematical concept that describes the rate and direction of motion of an object. It is represented by an arrow, with the length of the arrow representing the speed of the object and the direction of the arrow representing the direction of motion.

2. How is vector velocity different from scalar velocity?

Scalar velocity only describes the speed of an object, while vector velocity includes both the speed and direction of motion. Scalar velocity is represented by a single number, while vector velocity is represented by an arrow.

3. How do you calculate vector velocity?

Vector velocity is calculated by dividing the displacement vector (change in position) by the time interval in which the displacement occurs. This can be represented by the equation v = Δx/Δt, where v is the vector velocity, Δx is the displacement, and Δt is the time interval.

4. What are some real-life examples of vector velocity?

Some real-life examples of vector velocity include the motion of a car driving on a road, a bird flying in the sky, or a person walking in a particular direction. In each of these examples, the object has both a speed and a direction of motion.

5. How is vector velocity used in physics?

In physics, vector velocity is used to describe the motion of objects in both one and two dimensions. It is an important concept in understanding the laws of motion and can be used to calculate other important quantities, such as acceleration and displacement.

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