Answered: Purpose Mathematical models based on…

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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Question

Purpose

Mathematical models based on quadratic equations describe curved paths through space.

The purpose of this project is to develop an understanding of techniques used to apply quadratic models to describe motion.

Assignment Goal

Describe the motion of a rocket using a quadratic model.

Instructions:

Respond to each of the questions. Your solutions must document all of your work.
Scenario: A toy rocket is launched straight upward from a pad 10 ft above ground level with
an initial velocity of 80 ft/sec.
Use the general formula for the vertical position (height) of an object moving under the
influence of gravity ?= ―1
2??2 + ?0?+ ?0 where s0 is initial vertical position, v0 is initial
velocity, and s is vertical position of the object.

1. Define a model (equation) to express the vertical position (height) of the rocket s (in meters) above ground level t seconds after launch. Let g = 32 ft/sec2.

2. Graph your equation with time on the horizontal axis and height on the vertical axis. Let the values for time range from 0 to 10 seconds and the values for the height range from 0 to 200 feet. Include your graph in this response.

3. Refer to your graph in Question 2. Explain what the vertex, x-intercept, and y-intercept represent in the context of this problem.

4. Calculate the time(s) at which the rocket is at a height of 40 ft. (Round to 1 decimal place.) Is this the maximum height the rocket will reach? Justify your response

5. Calculate the time(s) at which the rocket is at a height of at least 85 ft above the ground.
Round to the nearest hundredth. Explain your answer.

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