In §1.7 (about the drums of atomic waste disconcertingly dropped to the ocean fl
ID: 2259834 • Letter: I
Question
In §1.7 (about the drums of atomic waste disconcertingly dropped to the ocean floor by the Atomic Energy Commission) it is mentioned that v(300) is about 45.1 ft/s. Use computer software of your choice to compute v(300) (in ft/s) to an accuracy of four deci nal places (±0.0001 ft/s). To make sure everyone computes the same answer, let's agree that c = 0.08 lbf . s/ft, B = 470.327 lbf, W = 527.436 lbf. As we saw in class, and as is discussed in § 1.7, we have w. V(t) = exp Of course, the depth y(t) at time t is v(t)V(s)ds. 0 Your goal is to accurately approximate the time tf for which y(4) 300 and to indicate V(4) = u(300) for this time ty. (Following the book, I am using V(t) for the velocity (speed of descent) as a function of time t, and v(y) for the velocity as a function of depth y.)Explanation / Answer
SOL)
%%% Matlab code %%
clc;
clear all;
close all;
format long
syms t s
C=0.08;
B=470.327;
W=527.436;
g=32.174;
v_t=(W-B)/C*(1-exp(-C*g*t/W));
y_s=int(v_t,0,s);
t_f=solve(y_s==300);
fprintf('time tf at which y(tf)=300 is %fsec ',t_f);
Vt_f=subs(v_t,t_f);
fprintf(' V(tf) = %f m/s ',Vt_f);
OUTPUT:
time tf at which y(tf)=300 is 13.265273sec
V(tf) = 44.748118 m/s