**Question:**An aircraft has a lift-off speed of 12.1 km/h. If the aircraft's acceleration is constant, what minimum time is required for the aircraft to be airborne after a takeoff run of 23.6 m?**Explanation:**This problem requires us to determine the minimum time needed for an aircraft to become airborne, given its lift-off speed and the distance of the takeoff run. To solve this, we can use equations from kinematics that describe motion with constant acceleration.First, convert the lift-off speed from kilometers per hour to meters per second:\[ 12.1 \, \text{km/h} = 12.1 \times \frac{1000 \, \text{m}}{3600 \, \text{s}} = 3.36 \, \text{m/s} \]Next, we will use the kinematic equation that relates distance (s), initial velocity (u), acceleration (a), and time (t):\[ s = ut + \frac{1}{2}at^2 \]Since the initial velocity (u) is 0 (the aircraft starts from rest), the equation simplifies to:\[ s = \frac{1}{2}at^2 \]Rearranging this equation to solve for the time (t):\[ t^2 = \frac{2s}{a} \]\[ t = \sqrt{\frac{2s}{a}} \]We need the acceleration (a), which we can find using the final velocity (v) and distance (s) with the kinematic equation:\[ v^2 = u^2 + 2as \]Again, since the initial velocity (u) is 0:\[ v^2 = 2as \]Solving for a:\[ a = \frac{v^2}{2s} \]Using the converted velocity (v = 3.36 m/s) and distance (s = 23.6 m):\[ a = \frac{(3.36 \, \text{m/s})^2}{2 \times 23.6 \, \text{m}} \]\[ a = \frac{11.29 \, \text{m}^2/\text{s}^2}{47.2 \, \text{m}} \]\[ a = 0.239 \, \text{m/s

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Description: **Question:**An aircraft has a lift-off speed of 12.1 km/h. If the aircraft's acceleration is constant, what minimum time is required for the aircraft to be airborne after a takeoff run of 23.6 m?**Explanation:**This problem requires us to determine

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An aircraft has a lift-off speed of 12.1 km/h. If the aircraft's acceleration is constant, what minimum time is required for the aircraft to be airborne after a takeoff run of 23.6 m?

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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