A particle P moves freely under gravity in the plane of a fixed horizontal axis Ox, which lies on horizontal ground, and a fixed vertical axis Oy. P is projected from O with a velocity whose components along Ox and Oy are U and V, respectively. P returms to the ground at a point C. (a) Determine, in terms of U, Vand g, the distance OC. B P passes through two points A and B, each at a height h above the ground and a distance d apart, as shown in the diagram (b) Write down the horizontal and vertical components of the velocity of P at A. (c) Hence determine an expression for d in terms of U, V, g and h. (d) Given that the direction of motion of Pas it passes through A is inclined to the horizontal at an angle 0, where tan e=, determine an expression for V in tems of g, d and h.

A particle P moves freely under gravity in the plane of a fixed horizontal axis Ox, which lies on horizontal ground, and a fixed vertical axis Oy. P is projected from O with a velocity whose components along Ox and Oy are U and V, respectively. P returms to the ground at a point C. (a) Determine, in terms of U, Vand g, the distance OC. B P passes through two points A and B, each at a height h above the ground and a distance d apart, as shown in the diagram (b) Write down the horizontal and vertical components of the velocity of P at A. (c) Hence determine an expression for d in terms of U, V, g and h. (d) Given that the direction of motion of Pas it passes through A is inclined to the horizontal at an angle 0, where tan e=, determine an expression for V in tems of g, d and h.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 6P: At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of...

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Question

A particle P moves freely under gravity in the plane of a fixed horizontal axis Ox, which lies
on horizontal ground, and a fixed vertical axis Oy. P is projected from O with a velocity whose
components along Ox and Oy are U and V, respectively. P returns to the ground at a point C.
(a) Determine, in terms of U, Vand g, the distance OC.
P passes through two points A and B, each at a height h above the ground and a distance d apart, as
shown in the diagram.
(b) Write down the horizontal and vertical components of the velocity of P at A.
(c) Hence determine an expression for d in terms of U, V, g and h.
(d) Given that the direction of motion of P as it passes through A is inclined to the horizontal at an
angle 0, where tan e =, determine an expression for V'in terms of g, d and h.

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