Jumping in Different Gravitational Fields
We are trying to figure out how high a person could jump
or how far a golf ball would go on other planets. We have the % of
Earth's gravity of other planets, but we are befuddled about
translating that into distances, or approximate distances. For
instance, a planet with 38% or 254% of Earth's gravity.
Take the percentages of gravity, make it a decimal (divide by 100) and
divide the earth distance by that decimal. As an example, a golf shot
that traveled 100 yards on earth will travel 300 yards on a planet with
33% the gravity of earth.
The distance a projectile will go on another [or any] planet (assuming
exactly the same angle of launch and initial speed) depends directly on
the time it spends in the air and that depends upon the gravity. Halve
the gravity and spend twice as long in the air. You will also go twice
as far as on earth.
The equation is of the form t = 2Voy/g where g is the acceleration of
gravity, Voy the staring speed in the vertical direction and t is the
time in the air. The 2 comes from the particle making a round trip (up
and then back down)
Of course, you will probably need to pitch the explanation a bit "lower"
for your students.
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Update: June 2012