In putting, the force with which a golfer strikes a ball is planned so that the

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 1.0 m long or short, in case the putt is missed.

Accomplishing this from an uphill lie (that is, putting the ball downhill, see (Figure 1) ) is more difficult than from a downhill lie.

To see why, assume that on a particular green the ball decelerates constantly at 1.7 m/s2 going downhill, and constantly at 2.8 m/s2 going uphill.

PART A
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 1.0 m short to 1.0 m long of the cup.

PART B
Suppose we have an downhill 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 1.0 m short to 1.0 m long of the cup.

Explanation / Answer

partA] by third equation of motion ,

u = sqrt(2as) = between sqrt(2.8*2*6) and sqrt(2*2.8*8)

=between 5.80 m/s and 6.69 m/s

partC] u = between sqrt(1.7*2*6) and sqrt(2*1.7*8)

=between 4.52 m/s and 5.22 m/s

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