Imagine a universe without gravity. Imagine yourself to be an astronaut
floating in space. In this universe, if you tossed a rock where there was
no air, it would just keep going.....forever. Because the rock would be
going at a constant speed, it would cover the same amount of distance in
each second.
The equation for distance traveled when motion is uniform is
x = vt
Solving for speed yields
v = x/t
Upon returning to earth, what happens when you drop a rock? For most of
us it simply falls to the earth. If you look more closely, you'll
also notice that the distance that the rock falls with each second increases!
Gravity is constantly increasing the rock's speed. The equation of the vertical
distance y fallen after t is:
y = (1/2)*gt2
where g is the acceleration of gravity. The falling speed v
after time t is
v = gt
What happens when you throw the rock sideways? The curved motion that
results can be described as the combination of two straight-line motions:
one vertical and the other horizontal. The vertical motion undergoes the
acceleration due to gravity, while the horizontal motion does not. The
secret to analyzing projectile motion is to keep two separate sets of "books":
one that treats the horizontal motion according to:
x = vt
and the other that treats the vertical motion according to
y = = (1/2)*gt2
Horizontal motion
-
When thinking about how far, think about x = vt.
-
When thinking about how fast, think about v = x/t.
Vertical motion
-
When thinking about how far, think about y = (1/2)*gt2
-
When thinking about how fast, thin about v = gt.
|
