Projectile Puzzle: Which Ball Stays in the Air Longer?

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SUMMARY

In the discussion regarding projectile motion, it is established that two balls thrown at different angles but reaching the same height will remain in the air for the same duration. The key factor is that both balls must have equivalent vertical components of velocity to achieve the same height, which leads to the conclusion that the time of flight is independent of the angle of projection when height is constant. The formula used to analyze this is Y - Y0 = Vy0t - 1/2gt², confirming that the vertical velocity component determines the time spent in the air.

PREREQUISITES
  • Understanding of basic physics concepts, particularly projectile motion
  • Familiarity with kinematic equations, specifically Y - Y0 = Vy0t - 1/2gt²
  • Knowledge of vertical and horizontal components of velocity
  • Grasp of gravitational acceleration (g) and its effects on motion
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  • Study the principles of projectile motion in detail
  • Learn about the derivation and application of kinematic equations
  • Explore the effects of different launch angles on projectile trajectories
  • Investigate real-world applications of projectile motion in sports and engineering
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of projectile motion and the factors affecting the time of flight of projectiles.

robvba
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Two balls are thrown in the air at different angles, but each reaches the same height. Which ball remains in the air longer?

a the one thrown at the steeper angle
b the one thrown at a shallower angle
c both remain in the air the same time
d need more information

I'm thinking that V must be greater for the lower angle ball. And V = V0 for both.
At first i thought that the time that an object spends in the air is proportional to its height.
However, I'm confused because using t=V0/g results in a greater t for the faster projectile.

Please help. Thank you
 
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Think about the vertical component of each balls velocity. What must they be if the balls reach the same height?
 
Using Y-Y0=Vy0t-1/2gt^2 for the vertical component, and considering that Vy0 will be different for both while the height is fixed, than the one with the greather Vy0 will spend more time in the air. However, given that the only vertical force acting on an object is gravity, they must spend the same amount of time in the air...?
 
Yes both balls must have the same vertical component of velocity. If that is true they must both spend the same time in the air.
 
Ok. So the speed and angle would result in a vertical velocity component that would be equivalent between the two. Thanks you
 

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