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An airplane starts from 4 m/s and accelerates down a runway at 3 m/s2 and covers 386 m before it takes off. Determine the time it takes.

An airplane starts from 4 m/s and accelerates down a runway at 3 m/s2 and covers 386 m before it takes off. Determine the time it takes.

Principles of Physics: A Calculus-Based Text
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
Chapter1: Introduction And Vectors
Section: Chapter Questions
Problem 69P: A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0...
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t term and the constant term including the positive or negative signs • example: o If 4 = 2 t+ 1/2 (8) t2 o Simplify 1/2 (8) = 4, subtract 4 from both sides and rearrange the terms to get 0 = 4t2 + 2t - 4 o now a = 4, b = 2, c = -4 o plug these into the quadratic formula and get the two solutions, one when we use the + and the other when we use the - in the formula, just before the square root. Usually we want the positive solution - (-2+v(22-4(4)(-4)).(2*4) = 0.78 (-2-V(22-4(4)(-4).(2*4) = -1.3
Transcribed Image Text:t term and the constant term including the positive or negative signs • example: o If 4 = 2 t+ 1/2 (8) t2 o Simplify 1/2 (8) = 4, subtract 4 from both sides and rearrange the terms to get 0 = 4t2 + 2t - 4 o now a = 4, b = 2, c = -4 o plug these into the quadratic formula and get the two solutions, one when we use the + and the other when we use the - in the formula, just before the square root. Usually we want the positive solution - (-2+v(22-4(4)(-4)).(2*4) = 0.78 (-2-V(22-4(4)(-4).(2*4) = -1.3
An airplane starts from 4 m/s and accelerates down a runway at 3 m/s2 and covers 386 m before it takes off. Determine the time it takes. Note, we still need x = vo t + 1/2 a t2, but the formula will still have t and t?. This is called a quadratic equation. Probably the best way to solve this is with the quadratic formula (your other choices are factoring, completing the square, graphing or numerical methods) -6±/b² –4ac t = 2a Steps: • Simplify as much as possible and arrange in descending order - that is, get everything on one side of the equation with a zero on the other side and rearrange the terms so that t2 comes first, t comes second and the constant term is last • the quad formula has a, b, and c which are the coefficients of the t2 term, the
Transcribed Image Text:An airplane starts from 4 m/s and accelerates down a runway at 3 m/s2 and covers 386 m before it takes off. Determine the time it takes. Note, we still need x = vo t + 1/2 a t2, but the formula will still have t and t?. This is called a quadratic equation. Probably the best way to solve this is with the quadratic formula (your other choices are factoring, completing the square, graphing or numerical methods) -6±/b² –4ac t = 2a Steps: • Simplify as much as possible and arrange in descending order - that is, get everything on one side of the equation with a zero on the other side and rearrange the terms so that t2 comes first, t comes second and the constant term is last • the quad formula has a, b, and c which are the coefficients of the t2 term, the
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