How Do You Calculate the Change in Velocity of a Tennis Ball?

[nesan]

Change in velocity, help please. :)

Homework Statement

A tennis ball’s initial velocity is 30 m/s . When struck by a tennis racquet, its velocity becomes 28 m/s [N30°W]. Determine the ball’s change in velocity.

The Attempt at a Solution

I've used the normal component method but I end up with approximately 15 m/s.

I've never worked with velocity so it's kind of difficult for me at the moment.

In the North direction, it is approximately 24 m/s and in the West direction it is approximately 14 m/s.

The answer sheet says

56 m/s [N15°W]

Any help would be much appreciated, thank you. <3

 

[berkeman]

Homework Statement

A tennis ball’s initial velocity is 30 m/s . When struck by a tennis racquet, its velocity becomes 28 m/s [N30°W]. Determine the ball’s change in velocity.

The Attempt at a Solution

I've used the normal component method but I end up with approximately 15 m/s.

I've never worked with velocity so it's kind of difficult for me at the moment.

In the North direction, it is approximately 24 m/s and in the West direction it is approximately 14 m/s.

The answer sheet says

56 m/s [N15°W]

Any help would be much appreciated, thank you. <3

Velocity is a vector quantity, so you need to calculate the difference in the velocity vectors. Note how the answer is a vector?


EDIT -- Do you know how to subtract vectors? It's the same as adding them -- you do it component-wise, and then convert back to polar form to match the answer in this question.

 

[nesan]

Velocity is a vector quantity, so you need to calculate the difference in the velocity vectors. Note how the answer is a vector?


EDIT -- Do you know how to subtract vectors? It's the same as adding them -- you do it component-wise, and then convert back to polar form to match the answer in this question.

Can you show me an example please?

I'm not sure if I know how to add them.

Thank you. :)

 

[berkeman]

Can you show me an example please?

I'm not sure if I know how to add them.

Thank you. :)

You need to subtract them to find the difference.

So if the initial velocity vector were (x,y) = (1,2) and the final velocity vector were (-2,-3), what would the (x,y) difference vector be? And what would it be when converted back into polar coordinates?

So just convert your initial and final velocity vectors from the polar coordinates given into rectangular coordinates, subtract them component-wise, and convert them back to polar form to match the final answer.