Physical Background
Physics we can meet in our daily life at every step. One of the exiting sides is the application of physical models to explain different kind of sportive activities. Different parts of physics like mechanics, aero- and hydrodynamics are involved. THese models can be used to explain sporting activities and also to improve sport results. In these short module long jump as a part of athletics was chooesen to be analyzed an to be simulated.
The following movie
shows you Mike Powell at his long jump world record from 1991. As you can see in this video the motion of long jump is, in a way, like the motion of throwing a ball.
We want to do so first, throw a ball, starting and landing on a horizontal line.
The throw of a ball has two different ways of motion. The ball has constant velocitiy in horizontal motion, but the ball is accelerated downwards due to gravity. Therefore the vector of velocity is changing direction all the time.
Activity
Look at the animation
and answer the following questions:
Task 1:
Vector v0
has two components. Try two write a formula for vx and vy
depending on the angle of throwing.
Task 2:
Is there a
point with velocity v = 0 m/s?
Task 3:
You want to
increase the range of the throw. What possibilities do you have?
Task 4:
Describe
what happens, if you increase the angle of the throw.
Task 5:
What is the
angle with maximum range?
Case Study
Really good athletes reach a horizontal velocitiy of about 9 meters per second. The athletes have to increase vertical velocity, therefore they have to decrease horizontal velocity.
Task 6:
What would be the horizontal and vertical velocity, if the athletes tried to jump at an angle of 45 degrees?
Task 7:
Is it possible to reach world record with a velocity of 9 m/s and an angle of 45°?
Now it is
time to take a closer look at the long jump motion. One of the differences
between throwing a ball and the motion of long jump is the position of the
centre of mass. The centre of mass is not in a horizontal line to the ground.
It is about one meter above the ground, near the belly button. Talking about the
motion of long jump means talking about the motion of the centre of mass. The
athletes start their jump in an upright position. The belly button is therefore
at a height of 1 m. In a way the jump ends sitting or lying on a horizontal
level of zero.
Reflection
Task 8:
What is the effect on maximum range, if the jump starts at a height of 1 m?
Task 9:
What does starting at 1 m mean for the best jumping angle?
Task 10:
Is it now possible to reach world record with a velocity of 9 m/s and best jumping angle?