Three dimensional collision with bowling ball and pin.

[unrulypanda]

Homework Statement

In order to convert a tough split in bowling, it is necessary to strike the pin a glancing blow as shown in the figure. Assume that the bowling ball, initially traveling at 15.0 m/s, has eight times the mass of a pin and that the pin goes off at 75° from the original direction of the ball.

(a) Calculate the speed of the pin.
(b) Calculate the speed of the ball just after collision.
(c) Calculate the angle θ through which the ball was deflected. Assume the collision is elastic and ignore any spin of the ball.

Homework Equations

MbVb+MpVp=MbVB+MpVP (Mb=mass of ball, Mp=mass of pin, Vp=initial velocity for pin, VP=final velocity for pin, Vb=initial velocity for ball, VB=final velocity for ball.)

The Attempt at a Solution

I have no idea how to even attempt this problem.

 

[daveb]

Try writing down your Conservation of Momentum equations

 

[unrulypanda]

Should I write down the formula first? Should I plug in the numbers and continue trying to cancel out unknown variables? The conservation of energy and momentum equations are realllllly long -_-

 

[darksyesider]

I would like too bump this-I have the same question!
I tried so far using the p=mv equation in both dimensions (since in the x direction it equals zero!), however I can't seem to solve for what they're asking…my algebraic manipulations aren't as well.

 

[CWatters]

This is in the homework section and the forum requires you to show your working/attempt. How else can we see where you are going wrong ;-)

Should I write down the formula first? Should I plug in the numbers and continue trying to cancel out unknown variables? The conservation of energy and momentum equations are realllllly long -_-

It's not usually a good ide to plug in the numbers early on.

 

[bobie]

the bowling ball, initially traveling at 15.0 m/s, has eight times the mass of a pin and that the pin goes off at 75° from the original direction of the ball.

Hi, I do not know if the formula for balls is valid for pins, if it is ...then
you know cos λ_p (75°) = 0.2588 and the ratio R_m of M_b to total mass 8/9
you get quickly v_p = v₀* cos λ* 2R (15*0.25*16/9) = 6.9 m/s
the you can easily find all missing data (with the E and p formulas.)

 

[CWatters]

The problem statement contains no information on the vertical dimension so this is really a 2D problem.