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(a) An aircraft starts from rest and taxis along the runway before taking off. The table below shows how the acceleration a ms-2 of the aircraft varies with time t seconds. 10.0 0.40 0.00 20.0 0.80 5.0 15.0 25.0 30.0 0.05 0.25 0.60 1.05 1.35 Use Simpson's rule to find: (i) the speed, in ms-, of the aireraft after 1.5 seconds. (ii) the distance, in metres, travelled by the aircraft in 1.5 seconds. (b) A function y satisfies the differential equation dy = T dx Given that y =1 when r = 0 and that y = 0.91 when r = 0.1, use the approximation dy 2h 2 Yn+1 - Yn-1, dr and a step length of 0.1 to find the value of y when r = decimal places. 0.4, giving your final answer correct to 3 3.

(a) An aircraft starts from rest and taxis along the runway before taking off. The table below shows how the acceleration a ms-2 of the aircraft varies with time t seconds. 10.0 0.40 0.00 20.0 0.80 5.0 15.0 25.0 30.0 0.05 0.25 0.60 1.05 1.35 Use Simpson's rule to find: (i) the speed, in ms-, of the aireraft after 1.5 seconds. (ii) the distance, in metres, travelled by the aircraft in 1.5 seconds. (b) A function y satisfies the differential equation dy = T dx Given that y =1 when r = 0 and that y = 0.91 when r = 0.1, use the approximation dy 2h 2 Yn+1 - Yn-1, dr and a step length of 0.1 to find the value of y when r = decimal places. 0.4, giving your final answer correct to 3 3.

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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An aircraft starts from rest and taxis along the runway before taking off. The table below shows how the acceleration a ms-2 of the aircraft varies with time t seconds. (a) 0.00 0.05 10.0 0.40 15.0 0.60 5.0 20.0 25.0 30.0 0.25 0.80 1.05 1.35 a Use Simpson's rule to find: (i) the speed, in ms-, of the aireraft after 1.5 seconds. (ii) the distance, in metres, travelled by the aircraft in 1.5 seconds. (b) A function y satisfiès the differential equation dy + y? = z?. dr Given that y = 1 when z = 0 and that y = 0.91 when z = = 0.1, use the approximation dy 2h A Y1+1 - Yn-1, dr and a step length of 0.1 to find the value of y when a = 0.4, giving your final answer correct to 3 decimal places. 3.
Transcribed Image Text:An aircraft starts from rest and taxis along the runway before taking off. The table below shows how the acceleration a ms-2 of the aircraft varies with time t seconds. (a) 0.00 0.05 10.0 0.40 15.0 0.60 5.0 20.0 25.0 30.0 0.25 0.80 1.05 1.35 a Use Simpson's rule to find: (i) the speed, in ms-, of the aireraft after 1.5 seconds. (ii) the distance, in metres, travelled by the aircraft in 1.5 seconds. (b) A function y satisfiès the differential equation dy + y? = z?. dr Given that y = 1 when z = 0 and that y = 0.91 when z = = 0.1, use the approximation dy 2h A Y1+1 - Yn-1, dr and a step length of 0.1 to find the value of y when a = 0.4, giving your final answer correct to 3 decimal places. 3.
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