In the hope that the Moon and Mars will one day become tourist attractions, a go
ID: 1836622 • Letter: I
Question
In the hope that the Moon and Mars will one day become tourist attractions, a golf course is built on each. An average golfer on Earth can drive a ball from the tee about 68% of the distance to the hole. If this is to be true on the Moon and on Mars, by what factor should the dimensions of the golf courses on the Moon and Mars need to be changed relative to a course on Earth? The Moon has no atmosphere, and the effects of the thin atmosphere on Mars can be neglected for this problem. The dimensions of the golf course on the Moon must be increased by a factor of____, whereas the dimensions for the golf course on Mars must be increased by a factor of _____.
Explanation / Answer
acceleration due to gravity on mars , gma = 3.73 m/s^2
acceleration due to gravity on moon , gmo = 1.67 m/s^2
acceleration due to gravity on earth , ge = 9.8 m/s^2
as the range of the projectile is given as
R = v^2 * sin(2 * theta)/g
for all other parameters to be same , only changing the acceleration due to gravity
On Moon,
dimensions of the golf course on the Moon must be increased by a factor = ge/gmo
dimensions of the golf course on the Moon must be increased by a factor = 9.8/1.67
dimensions of the golf course on the Moon must be increased by a factor = 5.87
the dimensions of the golf course on the Moon must be increased by a factor 5.87
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the dimensions for the golf course on Mars must be increased by a factor = ge/gma
the dimensions for the golf course on Mars must be increased by a factor = 9.8/3.73
the dimensions for the golf course on Mars must be increased by a factor = 2.63
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