May Encounter a Jump...
These were taken by Jason Hoisington
Did you know that the motion you travel off of a jump can be calculated
so you will know where you will land? Yes, it can. From projectile motion
kinematic equations values such as your velocity, max height, and farthest
distance can be calculated from these equations.
In the pictures above, I am going
off a jump that sent me off into the air in a parabola shaped path. I
did not start at the top of the hill because I wanted to walk away from
the hill in one piece, but I started half way up between the top and
the jump. I did have to hold onto the sled when I went off the jump,
other wise I would end up using my jeans as a sled instead.
There are angles which are helpful
to know when you want to make a jump, such as the one in the picture above.
Depending on what you are trying to do with the jump, there are angles
which give you the maximum height or the longest distance traveled. From
the picture below, you can see that at different angles, the object being
launched will reach different heights and land at different distances. The
graph below shows the distances and velocities just when the initial velocity
is 50 m/s. For different velocities you will reach different heights
and distances, but the maximum height, or "air" off the jump, will be reached
when it is at 90 degrees. Having a jump made at 90 degrees though, may not
be a practical thing to do. You will end up doing a face plant into a wall
of snow and ice which would hurt really bad, especially if you were traveling
very fast. Your best bet would to make as steep of a jump as possible through
trial and error that wouldn't cause you to smack into the jump and take it
out. This would hurt really bad, and would cause your friends to burst out
laughing in the snow once they saw that you were all right.
1. Main Page
(Serway and Jewett pg.87)
for the most distance is 45 degrees. At any other angle the distance is
shorter, as you can see from looking at the graph. What's interesting to
note is the angles 60 and 30 reach the same horizontal distance. Angles
75 and 15 also reach the same distance. The vector components of the
velocity in the x and y directions are independent of each other. The velocity
in the y direction changes with height and its position on the parabola
it makes because of the acceleration of gravity which always points down
in the -y direction. In the x direction there is no acceleration so the velocity
stays the same throughout the projectile motion of the object.
Some equations commonly used to
solve projectile/linear motion problems you may encounter, in case you want
to jump a creek or some other object and aren't sure what velocity or angle
you need to make it across:
(Serway and Jewett pg. 297)
Where V subscript
f is final velocity, Vsub i is initial velocity, a is acceleration due to
gravity (-9.81m/s²), t is time, x sub f is final distance, and x sub
i is the initial distance.
2. The Projectile Motion of a Sled off a Jump
3. The Mechanics of
4. How Much Energy Does it Take to Sled?