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Introductory Physics Homework Help
Solve Min Velocity for Ball Not to Touch Hemispherical Rock
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[QUOTE="012anonymousx, post: 4524454, member: 448434"] [h2]Homework Statement [/h2] A person standing at the top of a hemispherical rock of radius R kicks a ball (initially at rest on the top of the rock) to give it a horizontal velocity v. What is the minimum initial speed to ensure the ball doesn't touch the rock? [h2]Homework Equations[/h2] x^2 + y^2 = r^2 y = -0.5gt^2 + R [h2]The Attempt at a Solution[/h2] R - (gx^2)/(2v^2) > sqrt(R^2 - x^2). The left side is eqn for parabolic trajectory, the right is the boulder After a lot of math you get something like this: (g^2x^4) / (4v^4) + gRx^2 / v^2 + x^2 > 0 Now I am super confused about this part: For some reason, the claim goes like, as x approaches 0, we get the tightest limit, therefore it needs the largest curvature at the start and it will pass the boulder (reasonable I guess..). THEN for some reason, 1 > gR / v^2 I have no idea where this came from. See here; [url]http://minerva.union.edu/labrakes/2_D_Motion_Problems_Solutions.pdf[/url] Another solution I read was; m * v^2/R > mg Fc > Fg. Why...? The acceleration into the boulder has to be GREATER than gravity? That doesn't make a lot of sense to me :( [/QUOTE]
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Solve Min Velocity for Ball Not to Touch Hemispherical Rock
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