A particle moving in one dimension (the x-axis) is described by the wave function f psi(x) = { Ae^-bx, for x > 0 Ae^bx, for x < 0 where b = 2.00 m^-1, A > 0, and the +x-axis points toward the right, Determine A so that the wave function is normalized, Sketch the graph of the wave function, Find the probability of finding this particle in each of the following regions: within 50.0 cm of the origin, on the left side of the origin (can you first guess the answer by looking at the graph of the wave function?), between x = 0.500 m and x = 1.00 m.

Describe the path of a ray that approaches a mirror parallel to the principal axis.

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Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.