**Problem Statement:**An airplane has a mass of 100,000 kg and feels air friction at a force of 200,000 N. If the pilot wants to slow down from 120 m/s to 90 m/s in 2 minutes, what force should the engines exert? *Show your work.***Solution:**To solve this problem, we need to determine the total force required to achieve the desired deceleration and then calculate the force the engines must exert to counteract both the deceleration and the air friction. 1. **Calculate the deceleration:** - Initial velocity (u): 120 m/s - Final velocity (v): 90 m/s - Time (t): 2 minutes = 2 x 60 = 120 seconds Using the formula for acceleration (a = (v - u) / t):\[a = \frac{{90 \text{ m/s} - 120 \text{ m/s}}}{120 \text{ s}} = \frac{-30 \text{ m/s}}{120 \text{ s}} = -0.25 \text{ m/s}^2\] The negative sign indicates deceleration.2. **Determine the force needed for the deceleration:** Using Newton's second law (F = ma):\[F_{\text{deceleration}} = 100,000 \text{ kg} \times (-0.25 \text{ m/s}^2) = -25,000 \text{ N}\] The negative sign indicates the force is in the opposite direction of motion.3. **Determine the total force required, considering air friction:** The airplane also needs to overcome the air friction force of 200,000 N. Therefore, the total force the engines must exert (F_total):\[F_{\text{total}} = F_{\text{deceleration}} + 200,000 \text{ N}\] Substituting the values:\[F_{\text{total}} = -25,000 \text{ N} + 200,000 \text{ N} = 175,000 \text{ N}\]**Answer:**The engines should exert a force of 175,000 N to slow down the airplane from 120 m/s to 90 m/s in 2 minutes.

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An airplane has a mass of 100,000 kg, and feels air friction at a force of 200,000 N. If the pilot wants to slow down 120 m/s to 90 m/s in 2 minutes, what force should he have the engines exert? Show your work.

An airplane has a mass of 100,000 kg, and feels air friction at a force of 200,000 N. If the pilot wants to slow down 120 m/s to 90 m/s in 2 minutes, what force should he have the engines exert? Show your work.

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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