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.

 

[asteriatic]

I understand that velocity is a vector quantity that includes both magnitude (speed) and direction. In this problem, the initial velocity of the tennis ball is given as 30 m/s , meaning it is moving at a speed of 30 m/s in the South direction. When struck by the tennis racquet, the ball's velocity changes to 28 m/s [N30°W], meaning it is now moving at a speed of 28 m/s in a direction that is 30° west of North.

To determine the change in velocity, we can use vector subtraction. We can break down the initial and final velocities into their x and y components, where the x direction is East-West and the y direction is North-South.

Initial velocity: 30 m/s = 0 m/s [E] + (-30 m/s [N])
Final velocity: 28 m/s [N30°W] = 24.2 m/s [E] + 14 m/s [N]

To subtract these vectors, we can simply subtract their x and y components separately.
Change in velocity = (24.2 m/s - 0 m/s) [E] + (14 m/s - (-30 m/s)) [N]
= 24.2 m/s [E] + 44 m/s [N]
= 24.2 m/s [N26.6°E] (using Pythagorean theorem and trigonometry)

Therefore, the change in velocity is 24.2 m/s [N26.6°E]. This is equivalent to 56 m/s [N15°W], as stated in the answer sheet.

I hope this explanation helps you understand the concept of change in velocity and how to solve this type of problem. Remember to always break down vectors into their components and use vector addition or subtraction to determine the final result. Keep practicing and you will become more comfortable with working with velocity!