Projectile Motion: initial velocity problem

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SUMMARY

The discussion focuses on calculating the initial velocity of a projectile that returns to its launch level after 10.0 seconds and lands 300.0 meters away. The horizontal component of the initial velocity, calculated using the equation Δx = v0x * t, is determined to be 30 m/s. The challenge lies in finding the initial vertical component of velocity (v0y), which requires understanding the time of flight and the equations of motion under gravity. The key takeaway is that the time taken to reach the peak of the projectile's flight can be used to derive v0y.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with kinematic equations
  • Knowledge of gravitational acceleration (g = 9.81 m/s²)
  • Ability to manipulate algebraic equations
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  • Learn how to derive the initial vertical velocity using kinematic equations
  • Study the concept of time of flight in projectile motion
  • Explore the relationship between horizontal and vertical motion in projectiles
  • Investigate the effects of varying launch angles on projectile trajectories
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Homework Statement


Determine the initial velocity of a projectile that reuturns to launch level 10.0 seconds after it is launched and lands 300.0m away from the launch site.

Homework Equations


Δx=v0xt
Δy=v0yt+1/2gt2

The Attempt at a Solution


[/B] 300=v0x(10)
v0x=30m/s
I don't know how to procees with this problem since it appears that I'm missing v0y. I have time and the initial x component for velocity, but I don't know how I would use that to find the initial y component of velocity.
 
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The projectile (rather obviously) must take the same time to travel 300m horizontally as it does to travel vertically up and down.

So you know the time it takes to get to the top of the flight. You also know the acceleration and the final velocity at the top. Find an equation that gives you the initial vertical velocity.
 

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