In putting, the force with which a golfer strikes a ball is planned so that the
ID: 1527601 • Letter: I
Question
In putting, the force with which a golfer strikes a ball is planned so that the ball will stop within some small distance of the cup, say 2.00 m long or short, in case the putt is missed. Accomplishing this from an uphill lie (that is, putting the ball downhill, see the figure) is more difficult than from a downhill lie. (Figure 1)
Part A
To see why, assume that on a particular green the ball decelerates constantly at 1.5 m/s2 going downhill, and constantly at 2.1 m/s2 going uphill. Suppose we have an uphill lie 7.0 m from the cup. Calculate the allowable range of initial velocities we may impart to the ball so that it stops in the range 2.00 m short to 2.00 m long of the cup.
Express your answers using two significant figures separated by a comma.
Part B
Do the same for a downhill lie 7.0 m from the cup.
Express your answers using two significant figures separated by a comma.
Downhill lie m 7.0 7.0 m phill lie
Explanation / Answer
First consider the "uphill lie", in which the ball is being putted down the hill. Choose
x (o) to be the ball's original location, and the direction of the ball's travel as the positive direction. The final velocity of the ball is v(f) = 0 m/s , the acceleration of the ball is a = - 1.5 m/s^2, and the displacement of the ball will be 7±2 m, therefore, 5 m for the first case and 9 m for the second case
From
s={v(f)^2 –v(i)^2}/2a
initial velocity of the ball will be
v(i) = sqrt(2as) = sqrt(2•1.5•5) = 3.87 m/s
v(i) = sqrt(2as) = sqrt(2•1.5•9) = 5.2 m/s.
The range of acceptable velocities for the uphill lie is 3.87 m s to 5.2 m s , with a spread of 1.33 m/s.
Now consider the "downhill lie", in which the ball is being putted up the hill. Use a very similar setup for the problem, with the basic difference being that the acceleration of the ball is now a = - 2.1 m/s^2.
initial velocity of the ball
v(i) = sqrt(2as) = sqrt(2•2.1•5) = 4.58 m/s
v(i) = sqrt(2as) = sqrt(2•2.1•9) = 6.15m/s.
The range of acceptable velocities for the uphill lie is 4.58 m s to 6.15 m s , with a spread of 1.57 m/s.
Because the range of acceptable velocities is smaller for putting down the hill, more control in
putting is necessary, and so the downhill putt is more difficult.