Solving for 3 variables in projectile motion problem

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SUMMARY

The forum discussion focuses on solving a projectile motion problem involving a dart thrown at a 30-degree angle from a height of 1.6 meters, landing 20 meters away. Key equations include the vertical motion equation, y = y1 + Vy1t - 9.8t², and the relationship between initial velocity components, where the initial speed can be expressed in terms of horizontal (vx) and vertical (vy) components. The discussion emphasizes the need to isolate variables to find the initial speed, maximum height, and impact speed of the dart.

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  • Understanding of projectile motion principles
  • Familiarity with kinematic equations
  • Knowledge of trigonometric functions, specifically sine and cosine
  • Basic algebra for isolating variables
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  • Learn how to derive initial velocity components from angle and distance
  • Study the application of kinematic equations in two dimensions
  • Explore the concept of maximum height in projectile motion
  • Investigate the effects of initial height on projectile trajectories
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This discussion is beneficial for physics students, educators, and anyone interested in mastering projectile motion problems and applying kinematic equations effectively.

babacanoosh
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Homework Statement



A dart is thrown at a 30 degree angle above the horizontal from a height of 1.6 meters. It hits the ground 20 meters away.

a) find the initial speed?
b)what is the maximum height reached by the dart (relation to the ground)?
c)what is the speed of the dart as it hits the ground?






Homework Equations



y= y1 + Vy1t - 9.8t^2
Vy = Vy1^2 - 2(9.8)(y - y1)
Vy= Vy1 - 9.8t

The Attempt at a Solution



x1 = 20
x=0
t=?
a=-9.8
y1=?
y=?


I understand that I most likely need to use the following three equations in order to isolate one variable. I am not sure which variable/how to.
 
Physics news on Phys.org
Do you know what y1 (physically) means? Because its value is given in the problem.
So is that of y.

If you call the initial speed v, then you can rewrite v in terms of vx and vy and the angle (30 degrees).
 

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