45 Vs 60 Degree Angle

Maximum Range

Imagine a cannonball launched from a cannon at three unlike launch angles - 30-degrees, 45-degrees, and 60-degrees. The launch speed is held abiding; just the angle is changed. Imagine too that the cannonballs do not encounter a meaning amount of air resistance. How volition the trajectories of the iii cannonballs compare? Which missive will have the greatest range? Which cannonball volition reach the highest top meridian before falling? Which cannonball volition accomplish the ground commencement? The animation below depicts such a situation. The path of the cannonballs are shown. Additionally, the velocity components (horizontal and vertical) are represented by arrows in the animation.

Anim'n of 3 Projectiles at 30, 45, and 60-degree Launch Angle

As can be seen from the above animation, each missive follows a parabolic path. The cannonball launched at a 45-caste angle had the greatest range. The cannonball launched at a lx-caste angle had the highest meridian height earlier falling. The cannonball launched at the 30-degree angle reached the ground outset.

An analysis of the velocity components for these three projectiles reveals reasons for these observations. The top height of a projectile is adamant by the initial value of the vertical velocity component. The greater the initial value of five_y, the higher that a projectile will rising. The projectile launched at threescore-degrees has the greatest v_y, and as such the greatest peak height. The "hang time" of a projectile is too determined by the initial value of the vertical velocity component. The smaller the initial value of v_y, the shorter the hang time. The projectile launched at 30-degrees has the smallest v_y, and every bit such the shortest hang time. The range of a projectile is adamant past 2 parameters - the initial value of the horizontal velocity component and the hang time of the projectile. As can be seen from the animation, the projectile launched at sixty-degrees has the greatest hang time; however its range is limited by the fact that the v_x is the smallest of all three angles. The projectile launched at 30-degrees has the greatest v_xof all 3 launch angles; yet its range is limited past the fact that the hang time is so short. The projectile launched at 45-degree does not win in either category, however the fact that it is able to place a strong showing in each category contributes to its ability to achieve the greatest range. More sophisticated arguments for why the 45-degree launch angle yields the greatest range exist; yet since they involve the utilise of calculus, they are not presented here.

For more than information on physical descriptions of motion, visit The Physics Classroom Tutorial. Detailed data is available there on the following topics:

Projectiles
Characteristics of a Projectile'due south Trajectory

Describing Projectiles with Numbers

Initial Velocity Components