apollo astronaunts took a nine iron to the moon and hit a golf ball about 180 m ! Assuming that the swing, launch angle, and so on, were the same as on earth where the same astronaut could hit it only 35 m, estimate the acceleration due to gravity on the surface of the moon. (neglect air resistance in both cases, but on the moon there is none!)
To estimate the acceleration due to gravity on the surface of the moon based on the given information, we will make use of the projectile motion equation:
d = ((v^2) * sin(2θ)) / g
Where:
- d is the distance covered by the golf ball
- v is the initial velocity of the golf ball
- θ is the launch angle of the golf ball
- g is the acceleration due to gravity
Given that the astronaut can hit the golf ball 180 meters on the moon and only 35 meters on Earth, and assuming the swing, launch angle, and other factors remain the same, we can set up the following equation:
180 = ((v^2) * sin(2θ)) / g_moon
35 = ((v^2) * sin(2θ)) / g_earth
Since the swing and launch angle are the same in both cases, we can cancel them out. Now, let's solve for the acceleration due to gravity on the moon (g_moon):
180 * g_moon = 35 * g_earth
To simplify calculations, the acceleration due to gravity on Earth (g_earth) is approximately 9.8 m/s^2. Substituting that value into the equation:
180 * g_moon = 35 * 9.8
Now, we can solve for g_moon:
g_moon ≈ (35 * 9.8) / 180
Calculating this expression:
g_moon ≈ 1.9 m/s^2
Therefore, the estimated acceleration due to gravity on the surface of the moon is approximately 1.9 m/s^2.