What's Incorrect About Calculating Impulse in This Volleyball Spike Example?

[Ion1776]

What wrong with this problem?

A ball is traveling horizontally over a volleyball net when a player "spikes" it, driving it straight down to the ground. The ball's mass is 0.24 kg, its speed before being hit is 6.4 m/s and its speed immediately after the spike is 21 m/s. What is the magnitude of the impulse from the spike?

J=(.24kg)(21m/s)-(.24kg)(6.4m/s)=3.5

this is wrong, what's wrong

 

[Ion1776]

Still need some input on this please?

 

[Doc Al]

J=(.24kg)(21m/s)-(.24kg)(6.4m/s)=3.5

this is wrong, what's wrong

Impulse and momentum are vectors--you must take direction into account. Subtract them as vectors, not just numbers.

 

[Ion1776]

This probably sounds stupid but what do u mean by subtract them as vectors.

I know know what vectors are but...

 

[Doc Al]

This probably sounds stupid but what do u mean by subtract them as vectors.

I know know what vectors are but...

You just subtracted them as numbers--which means you treated them as if they pointed in the same direction.

To subtract vectors, draw yourself a diagram. The two vectors are perpendicular to each other. Or you can find their components and subtract them.

Hint: Subtracting is the inverse of adding. How would you add two perpendicular vectors?

 

[Ion1776]

again this sounds dumb, but would add these as vectors give you

(.48kg, 27.4m/s)

 

[Doc Al]

again this sounds dumb, but would add these as vectors give you

(.48kg, 27.4m/s)

No, that doesn't quite make sense.

I'll start you off. Let's call horizontal and vertical the x and y axes (like usual).

The initial momentum is:
mv = (.24 kg)*(6.4 m/s) = 1.54 kg-m/s in the + x direction
Expressed as a vector using components, it would be:
(1.54, 0)

The final momentum is
mv = (.24 kg)*(21 m/s) = 5.04 kg-m/s in the - y direction
Expressed as a vector using components, it would be:
(0, -5.04)

Now subtract those two momentum vectors and find the magnitude of the impulse.

 

[Ion1776]

Alright got it