A general equation for the height y of the mountain in terms of d , ϕ and θ .

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Portfolio Problem 3. A ball is thrown vertically upwards with a speed vo from the floor of a room of height h. It hits the ceiling and then returns to the floor, from which it rebounds, managing just to hit the ceiling a second time. Assume that the coefficient of restitution between the ball and the floor, e, is equal to that between the ball and the ceiling. Compute e.

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Chapter 1, Problem 39CP

To determine

A general equation for the height y of the mountain in terms of d, ϕ and θ.

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Portfolio Problem 3. A ball is thrown vertically upwards with a speed vo from the floor of a room of height h. It hits the ceiling and then returns to the floor, from which it rebounds, managing just to hit the ceiling a second time. Assume that the coefficient of restitution between the ball and the floor, e, is equal to that between the ball and the ceiling. Compute e.

Portfolio Problem 4. Consider two identical springs, each with natural length and spring constant k, attached to a horizontal frame at distance 2l apart. Their free ends are attached to the same particle of mass m, which is hanging under gravity. Let z denote the vertical displacement of the particle from the hori- zontal frame, so that z < 0 when the particle is below the frame, as shown in the figure. The particle has zero horizontal velocity, so that the motion is one dimensional along z. 000000 0 eeeeee (a) Show that the total force acting on the particle is X F-mg k-2kz 1 (1. l k. (b) Find the potential energy U(x, y, z) of the system such that U x = : 0. = O when (c) The particle is pulled down until the springs are each of length 3l, and then released. Find the velocity of the particle when it crosses z = 0.

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