Test the batting distance:
Lay the bat (ruler/paint stick) flat on the paper and hold it at one end with one hand, which will act as the pivot point, or fulcrum. Place the other hand on the bat near the pivot point, and use it to sweep the bat across the paper to hit the coin. Test how far the coin moves when it is struck by the end of the bat furthest from the pivot point. (The bat may not effectively hit the coin by it's tip, so use a point as far from the pivot point as possible that works well.) Make sure the paper is long enough to accommodate the majority of the coin hits from this furthest position. The bat should be drawn back to the same position each time before hitting the coin, to make the force consistent.
Mark up the paper and bat:
Mark a starting line across one end of the paper, which the coins will be laid on before they are hit by the bat. The pivot point of the bat will also be on this line.
Mark a line to which the bat is drawn back to before it hits the coin.
Mark 2, or maybe 3, positions along the length of the bat, one being near to the pivot point and one far from the pivot point (making sure that the far point is able to hit the coin effectively, and that the near point allows space for the fingers that draw the bat back).
Optional: mark the length of the paper with a scale, so the distance the coins move can be quickly read off. Alternatively, use a measuring tape to measure from the starting line how far the coin goes.
Hit the coin using different positions on the bat, and record data:
Place the pivot point of the bat on the starting line, and a coin on the paper next to one of the positions marked on the bat. Draw the bat back to the designated line, and hit the coin as hard as possible. Watch where the coin comes to rest. Discount the turn if the coin rolls on its edge, leaves the edge of the paper.
Practice hitting the coin with the bat from different positions, to get a consistent sweep and consistent force hitting the coin, then start recording data.
Record the distance travelled by the coin, using the scale at the side of the paper/a measuring tape. You can leave a few coins where they come to rest before recording several data points at once (though with too many coins, they are likely to hit previous ones).
Record multiple data points (10 or more) from the same starting position on the bat, to allow for hitting variability or random bumps in the paper. (Maybe rotate through the starting positions so that as hitting gets more effective there is no bias towards certain starting positions.)
Graph results. Class data can be pooled.
Conclusions and discussion:
Graphing the results (or simply colour coding the resting places of the coin so that the grouping according to starting position can be visualised) should show a general grouping according to the starting position. The groups may overlap.
The coin will, on average, go further when it is hit with the end of the bat furthest from the pivot point. This is because this part of the bat is moving with most speed when it hits the coin, and so hits the coin with greater force. The ruler/paint stick is acting as a class 3 lever. A greater force moving over a smaller distance near the pivot point results in a smaller force over a greater distance far from the pivot point. The greater distance moved by the tip means that it is moving faster, and can hit the coin with more speed.
Baseball bats and golf clubs use this principle: the end of the bat or club moves faster than our hands near the pivot point, and so can hit the ball further. Tennis racquets also use this principle, along with the elasticity of the racquet strings, to give the ball more speed.