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

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Homework Help Overview

The discussion revolves around the problem of launching a projectile to hit a target that is moving away from the launch point. The subject area includes kinematics and projectile motion.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss finding the x and y locations of the projectile as functions of time. There are attempts to derive an equation for the position of the target (P) based on these functions. Questions arise regarding the relationship between the projectile's trajectory and the target's position, particularly in terms of horizontal distance and height.

Discussion Status

Some participants have provided equations for the projectile's motion, while others are exploring how to relate these to the target's position. There is an ongoing inquiry into the necessary trigonometric relationships needed to connect the projectile's coordinates to the target's location.

Contextual Notes

Participants have noted the importance of not substituting specific values for gravitational acceleration (g) in their equations. There is also an emphasis on understanding the geometric relationships involved in the problem.

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
DSC_1158.JPG
 
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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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