Introduction
Projectile Motion Galileo is credited with the discovery of parabolic motion. He did experiments with falling bodies, from which he deduced the acceleration due to gravity and its independence of the body’s mass and discovered that projectiles follow parabolic paths. Examples of parabolic motion include the paths of a stone thrown into the air at an angle, a bullet shot from a gun and water sprayed from a hose. The basic fact here is that every object that falls freely under the action of the Earth’s gravity experiences an acceleration g that is directed vertically down. When an object is thrown horizontally from some height h above ground with some initial velocity, it will follow a curved path and eventually it will return to the…show more content… This data is recorded in the following table:
Angle Average Horizontal Distance (cm) Average Horizontal Distance (m)
20° 259.1 cm 0.2591 m
30° 296.3 cm 0.2963 m
40° 338.5 cm 0.3385 m
45° 337.0 cm 0.3370 m
50° 332.2 cm 0.3322 m
60° 286.3 cm 0.2863 m
70° 215.2 cm 0.2152 m
These values show that the optimum angle is between 40° and 45°; 45° is theoretically the optimum angle, but the error could alter this. On either side of 45° the average distance is relatively equal for distances at an equal difference in angle measure from forty-five. This is shown by the values for 40° and 50°, and 30° and 60°.
Using these values the initial velocity for each angle was found using these values for horizontal velocity and the following equation: dx= Vi2sin 2θ g
Where dx is horizontal velocity, Vi is initial velocity, θ is the angle measure, and g is acceleration due to gravity. This equation was solved for initial velocity to be:
Vi= dxgsin 2θ
The initial velocity at each angle is shown in the following table:
Angle Initial Velocity
20° 6.29 ms
30° 5.79 ms
40° 5.80 ms
45° 5.75 ms
50° 5.75 ms
60° 5.69 ms
70° 5.73