The acceleration due to gravity on the surface of the Moon is 1.7 m/s²
<h3>Further explanation</h3>
Acceleration is rate of change of velocity.
![\large {\boxed {a = \frac{v - u}{t} } }](https://tex.z-dn.net/?f=%5Clarge%20%7B%5Cboxed%20%7Ba%20%3D%20%5Cfrac%7Bv%20-%20u%7D%7Bt%7D%20%7D%20%7D)
![\large {\boxed {d = \frac{v + u}{2}~t } }](https://tex.z-dn.net/?f=%5Clarge%20%7B%5Cboxed%20%7Bd%20%3D%20%5Cfrac%7Bv%20%2B%20u%7D%7B2%7D~t%20%7D%20%7D)
<em>a = acceleration (m / s²)v = final velocity (m / s)</em>
<em>u = initial velocity (m / s)</em>
<em>t = time taken (s)</em>
<em>d = distance (m)</em>
Let us now tackle the problem!
<u>Given:</u>
![d_{moon} = 180 ~ m](https://tex.z-dn.net/?f=d_%7Bmoon%7D%20%3D%20180%20~%20m)
![d_{earth} = 32 ~ m](https://tex.z-dn.net/?f=d_%7Bearth%7D%20%3D%2032%20~%20m)
![g_{earth} = 9.8 ~ m/s^2](https://tex.z-dn.net/?f=g_%7Bearth%7D%20%3D%209.8%20~%20m%2Fs%5E2)
<u>Unknown:</u>
?
<u>Solution:</u>
The motion of the golf ball is a parabolic motion, then we can use the following formula to calculate the horizontal displacement of the ball.
![\large {\boxed {d = \frac{u^2 \sin 2 \theta}{g}} }](https://tex.z-dn.net/?f=%5Clarge%20%7B%5Cboxed%20%7Bd%20%3D%20%5Cfrac%7Bu%5E2%20%5Csin%202%20%5Ctheta%7D%7Bg%7D%7D%20%7D)
Let's use this formula to find a comparison of the motion of golf ball on earth and on the moon.
![d_{moon} : d_{earth} = \frac{u^2 \sin 2 \theta}{g_{moon}}} : \frac{u^2 \sin 2 \theta}{g_{earth}}}](https://tex.z-dn.net/?f=d_%7Bmoon%7D%20%3A%20d_%7Bearth%7D%20%3D%20%5Cfrac%7Bu%5E2%20%5Csin%202%20%5Ctheta%7D%7Bg_%7Bmoon%7D%7D%7D%20%3A%20%5Cfrac%7Bu%5E2%20%5Csin%202%20%5Ctheta%7D%7Bg_%7Bearth%7D%7D%7D)
![d_{moon} : d_{earth} = \frac{1}{g_{moon}}} : \frac{1}{g_{earth}}}](https://tex.z-dn.net/?f=d_%7Bmoon%7D%20%3A%20d_%7Bearth%7D%20%3D%20%5Cfrac%7B1%7D%7Bg_%7Bmoon%7D%7D%7D%20%3A%20%5Cfrac%7B1%7D%7Bg_%7Bearth%7D%7D%7D)
![d_{moon} : d_{earth} = g_{earth} : g_{moon}](https://tex.z-dn.net/?f=d_%7Bmoon%7D%20%3A%20d_%7Bearth%7D%20%3D%20g_%7Bearth%7D%20%3A%20g_%7Bmoon%7D)
![180 : 32 = 9.8 : g_{moon}](https://tex.z-dn.net/?f=180%20%3A%2032%20%3D%209.8%20%3A%20g_%7Bmoon%7D)
![g_{moon} = (32 \times 9.8) \div 180](https://tex.z-dn.net/?f=g_%7Bmoon%7D%20%3D%20%2832%20%5Ctimes%209.8%29%20%5Cdiv%20180)
![\large {\boxed {g_{moon} = 1.7 ~ m/s^2} }](https://tex.z-dn.net/?f=%5Clarge%20%7B%5Cboxed%20%7Bg_%7Bmoon%7D%20%3D%201.7%20~%20m%2Fs%5E2%7D%20%7D)
<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Physics
Chapter: Kinematics
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate , Sperm , Whale , Travel