Projectile motion max height problem

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SUMMARY

The discussion focuses on solving a projectile motion problem where a projectile is launched from ground level with an initial speed of 48.7 m/s. The objective is to find the launch angle such that the maximum height equals the horizontal range. Key equations utilized include Vocos(angle) for horizontal velocity and Vosin(angle) for vertical velocity. The solution involves applying kinematic equations to relate time, initial velocity, and angle to determine the required parameters.

PREREQUISITES
  • Understanding of kinematic equations in physics
  • Familiarity with projectile motion concepts
  • Knowledge of trigonometric functions (sine and cosine)
  • Ability to solve algebraic equations
NEXT STEPS
  • Study the derivation of projectile motion equations
  • Learn how to apply the range and height formulas in projectile motion
  • Explore the effects of varying launch angles on projectile trajectories
  • Investigate real-world applications of projectile motion in sports and engineering
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in mastering projectile motion problems in classical mechanics.

dmb325
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Homework Statement



A projectile is launched from ground level with an initial speed of 48.7 m/s. Find the launch angle (the angle the initial velocity vector is above the horizontal) such that the maximum height of the projectile is equal to its horizontal range. (Ignore any effects due to air resistance.)

Homework Equations



Vocos(angle)=Vx
Vosin(angle)=Vy


The Attempt at a Solution


(X, 0) and (X/2, Ymax)
 
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In my experience you can always solve these projectile motion questions with the high school method. Write x = vt for the horizontal part,
Vy = Viy + at AND y = Viy*t - ½at² for the vertical part.
In this problem you need all three equations because you have unknown t, Vi and the angle. Give it a try!
 

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