# Collision of 2 balls of different masses traveling opposite direction

Question

Two small balls A and B have masses 0.5kg and 0.2kg respectively. They are moving towards each other in opposited directions on a smooth horizontal table when they collide directly. Immediately before the collision, the spped of A is 3m/s and the speed of B is 2m/s. The speed of A immediately after the collision is 1.5m/s. The direction of the motion of A is unchanged as a result of the collision.

By modelling the balls as particles, find

(a) The speed of B immediately after the collision

(b) The magnitude of the impulse exerted on B after the collision

Equations

$$Ft=mv-mu$$

My Attempt

(a) Conservation of momentum would mean that the initial momentum must be equal to the final momentum.

$$Ft=mv-mu$$

$$(0.5\times3.0)-(0.2\times2.0)=(0.5\times1.5)-(0.2\times x)$$

$$1.1=0.75-(0.2\timesx)$$

$$x=11.3m/s$$

(b) I have no Idea where to start here, I think it's more a question of now knowing what it is asking for. Is it asking for my value for $$Ft$$?

Any help would be great Hootenanny
Staff Emeritus
Gold Member
You might want to check your arithmetic on question (a). Yes, (b) is just asking you for the impulse which is the quantity Ft.

Sorry let me do that

first bit again.

(a)

$$1.1=0.75-0.2x$$

$$1\frac{7}{15} = 0.26$$

$$x = 7.3m/s$$

I hope thats a bit better (b)

$$Ft=mu-mv$$

$$Ft=0.2\times2-0.2\times7.3 = 1.06Ns$$

Does that look a bit better?

Hootenanny
Staff Emeritus
Gold Member
Sorry let me do that

first bit again.

(a)

$$1.1=0.75-0.2x$$
Good $$1\frac{7}{15} = 0.26$$
Not so good, where's your x gone?
$$x = 7.3m/s$$
Take a sanity check, does this seem reasonable to you?

Sorry let me do that

first bit again.

(a)

$$1.1=0.75-0.2x$$

$$\frac{1.1}{0.75} = 1\frac{7}{15} = 0.2x$$

$$x = \frac{1\frac{7}{15}}{0.2} = 7\frac{1}{3}$$

I would have thought th answer to be around 3.5 as that would make all the initial and final figures equal...

Hootenanny
Staff Emeritus
Gold Member
$$1.1=0.75-0.2x$$
And this one,
$$\frac{1.1}{0.75} = 1\frac{7}{15} = 0.2x$$
Let me show you step by step,

1.1=0.75-0.2x

1.1-0.75 = -0.2x

$$x = \frac{1.1-0.75}{-0.2}$$

Do you follow?

Oh my word! I can't believe I did that! Thats a shocker haha. Cheers I follow that, and now with that I will get the correct answer for (b) thanks =]

Hootenanny
Staff Emeritus
A pleasure as always 