Physics - How the change in height affects a horizontally launched projectile

Topics: Trajectory, Trajectory of a projectile, Projectile Pages: 8 (921 words) Published: November 16, 2013
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1.0 Aim:
The aim of this experiment is to determine how the height of a horizontally launched projectile affects the projectiles range.

2.0 Theory:
Galileo showed an appreciation for the proper relationship between mathematics, theoretical physics, and experimental physics.

Galileo discovered that a parabola was the theoretically ideal trajectory of an accelerated projectile in the absence of friction and other disturbances. Galileo agreed that there are limits to the validity of this theory and noted that a projectile trajectory which was close to the size Earth could not be presented as a parabola but he believed that distances reached with the artillery used in his day would only have a slight impact to the parabolic representation. Using Galileo’s theory on projectile motion, we can deduce that projectile motion is made up of two motions. a) Horizontal component which is constant velocity

b) Vertical component which is constant acceleration.
In class, a computer simulator was used to answer questions and indicate any relationships between the change in certain variables and how that affected different results. Since the mass and angle of inclination were constant, there was no changes in data gathered that was effected by said variables. Through the computerized simulations, the class had gathered that as the height of the apparatus changed the time of flight increased and so did the horizontal range.

This graph shows the parabolic relationship between the change in the initial height and how it affects the horizontal range. The velocity of the ball as it leaves the apparatus can be calculated by the conservation of energy equation. Due to the metal balls spherical shape, rotational motion must also be taken into account so the equation changes. 3.0 Materials/Equipment:

Metal BallPlastic tube
Tray of sandRuler (30cm and 1m)
Writing utensils (pencils)
Tape measureSticky Tape

4.0 Risk Assessment
Risk
Solution
Stepping on the ball
Provide a clear path for the ball to continue on with a closed ending which prevents the ball being stepped on. Slipping on loose sand
Brush and collect any loose sand as the experiment is conducted. Collision with flying projectile
Performing the experiment with the line of projection aimed away of class mates will minimize the chance of injury or being caught in crossfire

5.0 Method
1. Position the tube on the edge of table.
2. Measure the height of the apparatus from the ground up to the exit point. 3. Determine the position on the tube from which the ball will be released. 4. Release the ball from this position and note the approximate point of landing; retrieve the ball. 5. Place the tray of sand at the approximate landing point. Ensure the surface of the sand is smooth. 6. Release the ball and retrieve it from the tray of sand. Measure how far the projectile travelled. 7. Smooth over the surface of the sand.

8. Repeat steps 4-7 changing the height of the apparatus after every 5th measurement.

6.0 Results
Tube height (m)
Ball distance (m)
0.2
0.43

0.415

0.43

0.42
0.42
0.535

0.52

0.51

0.5

0.525
0.625
0.675

0.68

0.675

0.68

0.68
0.868
0.79

0.77

0.79

0.785

0.78
0.92
0.817

0.777

0.767

0.79
1.01
0.79

0.825

0.805

0.815
1.51
0.865

0.865

0.885

0.9

0.885

6.1 Edited results

Tube height (m)
Average distance (m)
0.2
0.363
0.42
0.527
0.625
0.643
0.868
0.757
0.92
0.78
1.01
0.817
1.51
0.999

6.2 Raw results
Tube height (m)
Average distance (m)
0.2
0.42375
0.42
0.518
0.625
0.678
0.868
0.783
0.92
0.78775
1.01
0.80875
1.51
0.88

Using v = u + at, we can rearrange the equation to find the time which then can be used in the equation Delta x = Ux*t to deduce the horizontal range that should have been reached by the projectile....