Launching a projectile to hit a target moving away from the launch point

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SUMMARY

The discussion focuses on the mathematical modeling of a projectile's trajectory to hit a target moving away from the launch point. The equations for the projectile's position are established as x(t) = ut.cos(θ) and y(t) = ut.sin(θ) - (1/2)gt², where 'u' is the initial velocity, 'θ' is the launch angle, and 'g' is the acceleration due to gravity. Participants emphasize the need to determine the height of the projectile above the target point P and the horizontal distance from the projectile's position to point P to solve the problem effectively.

PREREQUISITES
  • Understanding of projectile motion equations
  • Familiarity with trigonometric functions
  • Knowledge of kinematic equations
  • Basic calculus for function analysis
NEXT STEPS
  • Explore the derivation of projectile motion equations in detail
  • Learn how to apply trigonometry to solve for heights and distances in projectile motion
  • Investigate the impact of varying launch angles on projectile trajectories
  • Study the concept of relative motion to understand moving targets
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Students in physics, engineers working on projectile dynamics, and anyone involved in motion analysis or game development requiring accurate trajectory calculations.

johnsmith122
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Homework Statement
A ball is launched at A with a speed u at an angle ϴ (from the horizontal). Show that if a point P moves so as to keep d/dt(tanα)=constant, then P will "catch" the ball at point B.
Relevant Equations
tanϴ =tanα+tanβ
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Your attempt appears to be a random sequence of equations, not directed towards solving the problem.
First, find the x and y location of the projectile as a function of time. Don't substitute a value for g, just leave it as g.
Using those equations, find an equation for the position of P as a function of time.
 
Thanks for the help. I found the x and y location of the projectile to be x(t)=ut.cosϴ and y(t)=ut.sinϴ-1/2gt^2 but I'm unsure as to how to find an equation for P using this.
 
johnsmith122 said:
Thanks for the help. I found the x and y location of the projectile to be x(t)=ut.cosϴ and y(t)=ut.sinϴ-1/2gt^2 but I'm unsure as to how to find an equation for P using this.
Just a bit of trig. What is the height of (x,y) above P? So what is the horizontal distance from (x,y) to P?
 

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