A student stands on the edge of a merry-go-round which rotates eight times a minute and has a radius of two meters one evening as the sun is setting. The student produces a shadow on the nearby building, (Assume that the +x-axis is to the right, the origin is at the center of the shadow's path along the building, and that the student's shadow is at its rightmost position at t = 0. Use the following as necessary: t. In your equations, let distance be in meters and time be in seconds. Do not include units in your answers.) (a) Write an equation for the position of the shadow (in m). x(t) = 2 cos m (b) Write an equation for the velocity of the shadow (in m/s).

A student stands on the edge of a merry-go-round which rotates eight times a minute and has a radius of two meters one evening as the sun is setting. The student produces a shadow on the nearby building, (Assume that the +x-axis is to the right, the origin is at the center of the shadow's path along the building, and that the student's shadow is at its rightmost position at t = 0. Use the following as necessary: t. In your equations, let distance be in meters and time be in seconds. Do not include units in your answers.) (a) Write an equation for the position of the shadow (in m). x(t) = 2 cos m (b) Write an equation for the velocity of the shadow (in m/s).

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.

Question

A student stands on the edge of a merry-go-round which rotates eight times a minute and has a radius of two meters one evening as the sun is setting. The student produces a shadow on the nearby building. (Assume that the +x-axis is to the right, the origin is at the center of the shadow’s path along the building, and that the student’s shadow is at its rightmost position at t = 0. Use the following as necessary: t. In your equations, let distance be in meters and time be in seconds. Do not include units in your answers.)

(a) Write an equation for the position of the shadow (in m).

x(t) = \(2 \cos \left[ \left(\frac{\pi}{6}t\right) - 1 \right]\)

(b) Write an equation for the velocity of the shadow (in m/s).

v(t) = ________ m/s

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