If a putter at X velocity hits a stationary golf ball, how far will it roll?

Question

I think I can pretty much figure this out except one important detail that I don't know how to include: the angle of the face of the putter.

mass of putter (m1): .1325kg
initial velocity of putter (v1): 1.253 m/s
Angle of face of putter: 3 degrees
mass of golf ball (m2): .0047kg
initial velocity of golf ball (v2): 0

I'm pretty sure I need to solve for v1(final) and v2(final) in this formula:

Conservation of Momentum: m1v1 + m2v2 = m1v1(final) + m2v2(final)

Then plug them into the Energy Conservation formula to find the velocity of v2(final)...

Energy conservation: (.5)m1v1^2 + (.5)m2v2^2 = (.5)m1v1(final)^2 + m2v2(final)^2

....but, I have no idea where, when, or how to account for the angle of the putter.....not all the energy from the putter is directed into the horizontal motion of the golf ball.

If anyone can help, I'd so greatly appreciate it. I've been working on this forever.

Answer 1

when using conservation of momentum, keep in mind that the velocities are vector quantities.
It doesn't matter if the face of the putter is up or down, the resultant velocity of the golf ball will be at an angle of 3 degrees. One other nuance is that the golf ball is a sphere, which means that some of the energy is converted into rotational energy of the golf ball plus the resultant velocity of the ball.

Using the conservation of momentum and conservation of energy, since you are assuming an elastic collision with the putter, just remember that the v2(final) will have a vertical component. If it is upward, the ball will fly upward to apogee and return, and the ball will experience an inelastic collision with the ground, which will dissipate the vertical component of energy. If downward, the ball will also dissipate the vertical energy into the ground. Assume upward if you want to use conservation of energy to compute the work done by gravity to apogee, this is the energy that will be lost when the ball strikes the ground.

Another interesting note: Since the problem is to find out how far the ball will roll, you also need the forces that will retard the ball so that the resultant kinetic energy is drained off by frictional work.

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