Analysis of Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and moves along a curved path under the influence of gravity. When an object is projected at an angle with the horizontal, it follows a parabolic trajectory. In this analysis, we will compare the ranges of four projectiles that are projected with the same speed at different angles: 20 degrees, 35 degrees, 60 degrees, and 75 degrees with the horizontal.

Factors Affecting Range

The range of a projectile is the horizontal distance it travels before hitting the ground. The factors that affect the range of a projectile are the initial speed and the launch angle. In general, for a given initial speed, the range will be maximized when the launch angle is 45 degrees. However, in this case, the angles of projection are different and we need to determine which angle will result in the longest range.

Analysis of Projectile Ranges

To compare the ranges of the four projectiles, we can use the range formula for projectile motion:

Range = (initial speed)^2 * sin(2*angle of projection) / acceleration due to gravity

Let's calculate the ranges for the given angles:

1. Angle of Projection: 20 degrees
Range = (initial speed)^2 * sin(2*20) / acceleration due to gravity

2. Angle of Projection: 35 degrees
Range = (initial speed)^2 * sin(2*35) / acceleration due to gravity

3. Angle of Projection: 60 degrees
Range = (initial speed)^2 * sin(2*60) / acceleration due to gravity

4. Angle of Projection: 75 degrees
Range = (initial speed)^2 * sin(2*75) / acceleration due to gravity

Comparison of Ranges

By calculating the ranges for the given angles, we can compare them and determine the angle that results in the longest range.

It is important to note that the range is directly proportional to the square of the initial speed. Therefore, if the initial speed is the same for all projectiles, the range will only depend on the launch angle.

Conclusion

Based on the calculations, we can determine which angle of projection will result in the longest range. By comparing the ranges for the given angles, we find that the range will be the longest for the projectile launched at an angle of 35 degrees with the horizontal. Therefore, among the given angles, the person who projects the projectile at 35 degrees will achieve the maximum range.

answer is 35 degree