On the earth, you throw an object up in the air at some velocity, v, and it reaches a maximum vertical displacement (max. height if you prefer) of 4.8 meters. If you went to the moon, where the value of the gravitational acceleration of the moon is 1/6 of that on earth, and launched the object upwards at a velocity of 3.9 v (another words, increase v by a factor of 3.9), what would be the maximum vertical displacement it reaches on the moon in meters? (Hint: this is easiest done with proportions.)

Question

On the earth, you throw an object up in the air at some velocity, v, and it reaches a maximum vertical displacement (max. height if you prefer) of 4.8 meters.  If you went to the moon, where the value of the gravitational acceleration of the moon is 1/6 of that on earth, and launched the object upwards at a velocity of 3.9 v (another words, increase v by a factor of 3.9), what would be the maximum vertical displacement it reaches on the moon in meters?  (Hint:  this is easiest done with proportions.)

Henry · Answer

h = (Vf^2 - Vo^2) / 2g = 4.8m, h = (0 - Vo^2) / 19.6 = 4.8, Vo^2 / 19.6 = 4.8, Vo^2 = 19.6 * 4.8 = 94.08, Vo = 9.7m/s on earth. Vo = 3.9 * 9.7 = 37.83m/s on the moon. g = 9.8 / 6 = 1.63 on the moon. h = (37.83)^2 / 3.26 = 439m on the moon.