# Unit Vectors Homework: Write Vector Expression for Golf Ball Position

• Jbright1406
In summary, the position of a golf ball hit off a tee at the edge of a cliff can be expressed as a vector function of time, using unit vectors i and j. The x component is (16.0 m/s)t and the y component is (3.30 m/s)t - (4.90 m/s2)t^2. The position vector can be written as (16.0t) i + [(3.30t)-(4.9t^2)] j.
Jbright1406

## Homework Statement

A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by the following expressions.
x = (16.0 m/s)t
y = (3.30 m/s)t - (4.90 m/s2)t^2

Write a vector expression for the ball's position as a function of time, using the unit vectors i and j. (Use t, i and j as necessary.)

## The Attempt at a Solution

The best i am coming up with is
(19.30 m/s)t i - (4.90 m/s^2)t^2 j

I know I am missing something about the conversion but i don't know what, and am really confused about vectors

EDIT: I realized what i did. I get really confused with the vectors. i didnt realize the two x was going to compose the i component and the y was going to compose the j component. Thank for the help, but TBH I am glad a figured it out on my own...im sure ill remmeber now! Thanks
(16.0t) i + [(3.30t)-(4.9t^2)] j

Last edited:
Why did you just drop the (3.30 m/s)t part from the j component?

Writing a position vector with i,j (and sometimes) k is just writing everything in the same equation, basically, with an i after the x component, a j after the y, and a k after the z. This is what it boils down to, there's a bit more to it than that and if you have any specific questions I could try to help with that.

I didnt just drop the 3.3 i added it to the 16.0; i realized where i was mistaken at. check out the edit i just posted after you answered! Thank you for your help though! :-)

Last edited:

## What is a unit vector?

A unit vector is a vector with a magnitude of 1 and is used to indicate direction. It is often denoted by adding a hat (^) over the variable, such as ̂v.

## How do you write a vector expression for golf ball position?

The position of a golf ball can be expressed as a vector by using the coordinates of its position. For example, if the ball is located at (2,3) on a coordinate plane, the vector expression would be ̂r = 2i + 3j, where i and j represent the unit vectors for the x and y axes, respectively.

## Why is it important to use unit vectors in physics?

Unit vectors are important in physics because they allow us to specify the direction of a vector without being affected by its magnitude. This makes it easier to perform calculations and analyze physical phenomena.

## What is the difference between a position vector and a displacement vector?

A position vector describes the location of an object in reference to a fixed point, while a displacement vector describes the change in position of an object from its initial position to its final position.

## Can you write a vector expression for a golf ball's velocity?

Yes, the velocity of a golf ball can be expressed as a vector by taking the derivative of its position vector with respect to time. So if ̂r represents the position vector, then the velocity vector would be ̂v = d̂r/dt.

Replies
3
Views
374
Replies
9
Views
1K
Replies
2
Views
2K
Replies
19
Views
2K
Replies
4
Views
2K
Replies
12
Views
1K
Replies
52
Views
4K
Replies
2
Views
2K
Replies
14
Views
6K
Replies
14
Views
2K