It's the year 2103. It is a bright, clear, air-free afternoon on the Moon. A professional golfer at the first tee is about to address his or her ball. The hole is about 1900 yards (1740 m) away from where the golfer is currently standing. A deep crater is located directly behind the green, which is sloping away from where the golfer is currently standing. The golfer believes that it is possible for him or her to reach the green in two strokes. Which golf club, the 1-Wood (10.5 degree lie angle), 3-Wood (15.0 degree lie angle), 5-Wood (21.0 degree lie angle), or 7-Wood (25.0 degree lie angle), would set him or her up for the easiest chip possible. If the maximum possible initial velocity of the golf ball is 140 miles-per-hour (62.6 m/s), which is created by a maximum swing of 100 miles-per-hour (44.7 m/s) at the time of contact, which golf club would the golfer use in order to ensure the easiest second shot without changing his or her maximum swing, without risking a penalty shot, and without losing a golf ball in the crater?
[ Hint: Assume that there is no interference in the projectile motion of the golf ball from any other outside sources besides gravity (whose acceleration on the Moon is 1.63 m/s^2). Assume that there is no drag present due to the dimples and spin of the ball. Assume that the ball is hit cleanly in the "sweet spot" and travels straight.]
Since a deep crater is located directly behind the green, and since the green slopes away from him or her, if the golfer over-shoots the hole, the ball will end up in the crater, thus resulting in a penalty stroke and a lost ball. He or she must have the ball land before the hole, which is about 1900 yards (1740 m). In order to calculate the maximum distance traveled by the golf ball, the following equation may be used:
[ Picture of the lie angle for the 1-Wood taken by Patrick Kennery, 2003 ]
Range = ( ( initial velocity )^2 / ( acceleration due to gravity ) ) ( sin 2 ( initial angle ) )
Range = ( ( 62.6 m/s )^2 / ( 1.63 m/s^2 ) ) ( sin 2 ( 10.5 degrees ) )
Range = ( ( 3920 m^2/s^2 ) / ( 1.63 m/s^2 ) ) ( sin ( 21.0 degrees ) )
Range = ( 2400 m ) ( 0.358 )
Range = 859 m
[ Picture of the lie angle for the 3-Wood taken by Patrick Kennery, 2003 ]
Range = ( ( initial velocity )^2 / ( acceleration due to gravity ) ) ( sin 2 ( initial angle ) )
Range = ( ( 62.6 m/s )^2 / ( 1.63 m/s^2 ) ) ( sin 2 ( 15.0 degrees ) )
Range = ( ( 3920 m^2/s^2 ) / ( 1.63 m/s^2 ) ) ( sin ( 30.0 degrees ) )
Range = ( 2400. m ) ( 0.500 )
Range = 1200 m
[ Picture of the lie angle for the 5-Wood taken by Patrick Kennery, 2003 ]
Range = ( ( initial velocity )^2 / ( acceleration due to gravity ) ) ( sin 2 ( initial angle ) )
Range = ( ( 62.6 m/s )^2 / ( 1.63 m/s^2 ) ) ( sin 2 ( 21.0 degrees ) )
Range = ( ( 3920 m^2/s^2 ) / ( 1.63 m/s^2 ) ) ( sin ( 42.0 degrees ) )
Range = ( 2400. m ) ( 0.669 )
Range = 1610 m
[ Picture of the lie angle for the 7-Wood taken by Patrick Kennery, 2003 ]
Range = ( ( initial velocity )^2 / ( acceleration due to gravity ) ) ( sin 2 ( initial angle ) )
Range = ( ( 62.6 m/s )^2 / ( 1.63 m/s^2 ) ) ( sin 2 ( 25.0 degrees ) )
Range = ( ( 3920 m^2/s^2 ) / ( 1.63 m/s^2 ) ) ( sin ( 50.0 degrees ) )
Range = ( 2400. m ) ( 0.766 )
Range = 1840 m
In order to not over-shoot the hole and lose the ball in the crater, the golfer should choose to use his or her 5-Wood, whose range is 1610 meters, leaving a second shot of only 130 meters in length, in order to reach the green. If the golfer chooses the 7-Wood, the ball has a good chance of over-shooting the hole and landing in the crater. If the golfer chooses the 1-Wood or 3-Wood, he or she would not have as short of a second shot than if he or she chooses the 5-Wood.
[ The calculations and assumptions used in solving this problem will not hold true if this golfer were to play on Earth, or any other planet, that has an atmospheric air layer. Outside factors, including wind resistance, drag, lift, and spin, would become a factor in this calculation. Also, at this point in time, golfing on the Moon is not possible without a heavy space suit and Oxygen tank, which would inhibit his or her range of motion.]