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Introductory Physics Homework Help
Projectile motion: find distance a ball would land
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[QUOTE="phys1213, post: 5462182, member: 592418"] [h2]Homework Statement [/h2] I'm trying to come up with an equation to determine where a ball would land (basically the distance it moves) from a spring loaded projectile launcher set up on a table. I'm looking for "d", and I know the spring constant, compression, mass of the ball, height the ball starts at, angle the launcher is set at, and whatever else I can measure using a meter stick, balance, and protractor. There aren't any numbers just known variables [h2]Homework Equations[/h2] Conservation of Energy eqn (at least the version I learned in class): E[SUB]final[/SUB]-E[SUB]intial[/SUB]=E[SUB]input[/SUB]-E[SUB]output[/SUB] F=ma F[SUB]g[/SUB]=mg sinθ=v[SUB]oy[/SUB]/v[SUB]o[/SUB] cosθ=v[SUB]ox[/SUB]/v[SUB]o[/SUB] KE: 1/2mv[SUP]2[/SUP] Spring: 1/2kx[SUP]2[/SUP] [h2]The Attempt at a Solution[/h2] I attempted to use conservation of energy but I get stuck trying to figure out where d goes into be able to solve for it. Also, other online resources use a conservation of energy eqn that has different terms than what I was taught, but I'm assuming they are all the same. System: Ball and Earth Initial time: just after ball leaves launcher final time: just before ball hit ground E[SUB]final[/SUB]=1/2mv[SUB]f[/SUB][SUP]2[/SUP] E[SUB]initial[/SUB]= 1/2mv[SUB]o[/SUB][SUP]2[/SUP]+1/2kx[SUP]2[/SUP]+mgH E[SUB]input[/SUB]-E[SUB]output[/SUB]=0 1/2mv[SUB]f[/SUB][SUP]2[/SUP]-1/2mv[SUB]o[/SUB][SUP]2[/SUP]-1/2kx[SUP]2[/SUP]-mgH=0 And then I'm stuck trying to figure out how the distance goes into this. I'm wondering whether I need to integrate the velocity with respect to time and relate that to the distance since the distance the ball travels is the velocity*time. Any help is appreciated! [/QUOTE]
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Projectile motion: find distance a ball would land
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