Calculate Angle of Deflection for Curling Stone Collision

[monkeygrif]

Homework Statement

A curling stone thrown takes 4.8 s to travel 60 m. The stone collides with another stone. The collision is a glancing one. If the second stone is deflected 25° and travels 1.5 m/s, calculate the angle of deflection of the first stone after collision. Omit any effects due to friction.

Homework Equations

ρbefore = ρafter

The Attempt at a Solution

I looked at splitting it up into the x and y directions, but couldn't get anywhere. I looked in the answer key, and its 3.3 degrees, but I have no idea how to get there. Thanks!

 

[TSny]

Hello, monkeygrif. Welcome to Physics Forums.

You have the right idea of setting up x and y components of momentum conservation.

Can you show more detail of your attempt?

 

[monkeygrif]

Thanks!

x dir:

0 = mass(a)v2(a) + m(b)v2(b)

because of the wording of the question, i made the assumption that they had the same masses, and thus the masses were irrelevant, so:

0 = v2(a) + v2(b)

0 = v2(a)cosx - 1.5cos25

v2(a)cosx = 1.5cos25

y-dir:

same setup here, which ends up with:

v1(a) = v2(a) + v2(b)
12.5 = v2(a)sinx + 1.5sin25
v2(a)sinx = 11.87

from there i used the tangent ratio, tanx = opposite/adjacent, which gave me the x value of 83.4 degrees

 

[TSny]

OK. Looks pretty good. But note that you are taking the initial direction of motion of the first stone to be in the y-direction. That's fine. But then that means the deflection angles are measured with respect to the y-axis (not the x-axis). So, you'll need to think about whether you should use cosine or sine to get x-components. Similarly for y-components.

 

[monkeygrif]

Thanks so much! Its all worked out now. :)