Projectile Motion initial speed

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SUMMARY

The discussion centers on the launch angles of an ideal projectile and their relationship to range. It is established that for a given initial speed, there is only one optimal angle of 45 degrees that maximizes range in two-dimensional motion. However, there are two additional angles that yield the same range. In three-dimensional motion, the number of possible launch angles becomes infinite, contingent upon the definition of range used. The conversation highlights the complexity of projectile motion and the varying interpretations of range in different dimensions.

PREREQUISITES
  • Understanding of basic physics concepts, specifically projectile motion.
  • Familiarity with two-dimensional and three-dimensional motion principles.
  • Knowledge of the mathematical relationship between launch angle and range.
  • Ability to interpret vector definitions in physics.
NEXT STEPS
  • Research the mathematical derivation of projectile motion equations.
  • Explore the concept of range in three-dimensional projectile motion.
  • Study the effects of air resistance on projectile trajectories.
  • Learn about optimization techniques for maximizing projectile range.
USEFUL FOR

Students of physics, educators teaching projectile motion, and anyone interested in the mathematical modeling of motion in two and three dimensions.

jsr219
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For the initial speed of an ideal projectile, how many launch angles equal for the range of the projectile


-1

-2

-more than 2 but an infinite number of

-only one if the angle is 45 but other wise only 2

-an infinite number
 
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jsr219 said:
For the initial speed of an ideal projectile, how many launch angles equal for the range of the projectile -1

-2

-more than 2 but an infinite number of

-only one if the angle is 45 but other wise only 2

-an infinite number

Homework Statement


Homework Equations


The Attempt at a Solution


In 2 dimensional motion. that is -only one if the angle is 45 but other wise only 2 but if you thinking of 3d then there are infinite possible paths* as shown in images shown by Spinnor.

*I am not 100% sure in 3d case(I have read very little about it) because it depends on what's definition of range final position vector - initial position vector(if so then my answer is wrong) or minimum distance between final and initial position (if so then my answer is correct). can anybody please confirm me what's range definition.
 

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