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GR0177 #24
Problem
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Mechanics}Kinematics

If a stone is thrown at such an angle at an initial velocity, its horizontal vs t graph should be constant and positive . Thus, choices (A) and (E) are out.

Recalling the basic kinematics equation , one eliminates choice (D), since that shows a parabolic time dependence, when a linear one is required. Since the slope is negative, the -graph should look like III one has choice (C).

(If one forgets the basic equations above, one can derive it all from summing up the net force . Integrate both sides to get velocity. Integrate again to get position.)  Alternate Solutions
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 johnhero20102012-10-08 02:45:31 Since air resistance is being ignored, there is no force in the horizontal direction. Therefore, the x-component of the particle's velocity is constant. We are told that the stone is thrown in the +x direction. Therefore, the ( v_x) component of the velocity must be positive. Therefore, graph II represents (v_x) versus (t) . The y-component of the particle's velocity vector is initially positive, but it decreases at a constant rate due to the force of gravity, and eventually becomes negative. Therefore, graph III represents (v_y) versus (t) . Therefore, answer (C) is correct. Reply to this comment secretempire12012-08-28 08:13:12 If you consider just the vertical velocity of the stone, this problem becomes very simple. You initially toss the stone up, so the y velocity is initially some positive number. This rules out I and V. As gravity acts on the stone, it gets slower and slower and slower until it reaches zero. Then it starts falling, giving it a negative y velocity. The only graph that represents this behavior is III. And only choice C offers graph III as the choice for the y velocity.Reply to this comment isentropic2008-10-17 08:24:26 You could also plot the parabolic trajectory of the stone on an xy-plane and draw the velocity components. From there, it should be pretty easy to determine what the vt-graphs should look like.Reply to this comment antithesis2007-10-01 11:54:01 Actually, in this case, if you only look at , and realize it is case III, the only answer is (C), and you don't even need to consider Reply to this comment Actually, in this case, if you only look at , and realize it is case III, the only answer is (C), and you don't even need to consider     LaTeX syntax supported through dollar sign wrappers $, ex.,$\alpha^2_0$produces . type this... to get...$\int_0^\infty\partial\Rightarrow\ddot{x},\dot{x}\sqrt{z}\langle my \rangle\left( abacadabra \right)_{me}\vec{E}\frac{a}{b}\$