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Problem 2: We discussed gravitational acceleration near the ground to be a constant g, which gives the position of an object in free fall as quadratic in time. Let's say that, in the remote future, a cataclysmic event has destabilised the Earth's interior, and the planet is disintegrating. The gravity near the surface of the collapsing Earth is then found as: Iomt(t) = ge¬at², where t > 0 is time, a 2 0 is some constant, and g is the original surface gravitational acceleration. During the cataclysm, a small rock was ejected straight off the surface at some speed vo at time t = 0. The near-surface gravity, however, was still strong enough that it started pulling the rock back. Unlike the constant surface gravity case, however, notice limț-→∞ Gomt (t) = 0, implying that this rock will have a terminal velocity it will settle into. What is the rock's terminal speed v»? When calculating vV, you may run into a definite integral that is not easily solvable. Fortunately, this is a well-known and important result in STEM. You may search up this integral, and write a brief paraphrase of how your source solves the integral. BTW, the indefinite counterpart of the integral is not known as a closed form, so make sure you have a definite integral set up.

Problem 2: We discussed gravitational acceleration near the ground to be a constant g, which gives the position of an object in free fall as quadratic in time. Let's say that, in the remote future, a cataclysmic event has destabilised the Earth's interior, and the planet is disintegrating. The gravity near the surface of the collapsing Earth is then found as: Iomt(t) = ge¬at², where t > 0 is time, a 2 0 is some constant, and g is the original surface gravitational acceleration. During the cataclysm, a small rock was ejected straight off the surface at some speed vo at time t = 0. The near-surface gravity, however, was still strong enough that it started pulling the rock back. Unlike the constant surface gravity case, however, notice limț-→∞ Gomt (t) = 0, implying that this rock will have a terminal velocity it will settle into. What is the rock's terminal speed v»? When calculating vV, you may run into a definite integral that is not easily solvable. Fortunately, this is a well-known and important result in STEM. You may search up this integral, and write a brief paraphrase of how your source solves the integral. BTW, the indefinite counterpart of the integral is not known as a closed form, so make sure you have a definite integral set up.

College Physics
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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Problem 2: We discussed gravitational acceleration near the ground to be a constant g, which gives the position of an object in free fall as quadratic in time. Let's say that, in the remote future, a cataclysmic event has destabilised the Earth's interior, and the planet is disintegrating. The gravity near the surface of the collapsing Earth is then found as: Iomt (t) = ge-at², where t > 0 is time, a 2 0 is some constant, and g is the original surface gravitational acceleration. During the cataclysm, a small rock was ejected straight off the surface at some speed vo at time t = 0. The near-surface gravity, however, was still strong enough that it started pulling the rock back. Unlike the constant surface gravity case, however, notice lim Jomt (t) = 0, implying that this rock will have a terminal velocity it will settle into. What is the rock's terminal speed v»? When calculating v0, you may run into a definite integral that is not easily solvable. Fortunately, this is a well-known and important result in STEM. You may search up this integral, and write a brief paraphrase of how your source solves the integral. BTW, the indefinite counterpart of the integral is not known as a closed form, so make sure you have a definite integral set up. BONUS: Numerically (i.e. using software) compute and make a plot of v(t).
Transcribed Image Text:Problem 2: We discussed gravitational acceleration near the ground to be a constant g, which gives the position of an object in free fall as quadratic in time. Let's say that, in the remote future, a cataclysmic event has destabilised the Earth's interior, and the planet is disintegrating. The gravity near the surface of the collapsing Earth is then found as: Iomt (t) = ge-at², where t > 0 is time, a 2 0 is some constant, and g is the original surface gravitational acceleration. During the cataclysm, a small rock was ejected straight off the surface at some speed vo at time t = 0. The near-surface gravity, however, was still strong enough that it started pulling the rock back. Unlike the constant surface gravity case, however, notice lim Jomt (t) = 0, implying that this rock will have a terminal velocity it will settle into. What is the rock's terminal speed v»? When calculating v0, you may run into a definite integral that is not easily solvable. Fortunately, this is a well-known and important result in STEM. You may search up this integral, and write a brief paraphrase of how your source solves the integral. BTW, the indefinite counterpart of the integral is not known as a closed form, so make sure you have a definite integral set up. BONUS: Numerically (i.e. using software) compute and make a plot of v(t).
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