Question

3. (10 marks) Suppose you measured the speed of a shuttlecock falling, and got the following data points time (s) velocity (m/s) 0.25 3.3 0.5 0.75 4.8 5.5 5.9 1.25 1.5 1.75 (a) Use a Riemann sum to approximate the total distance travelled by the shuttlecock (b) Use the trapezoidal rule to approximate the total distance travelled by the shuttlecock. (c) Use the central difference formula to approximate the acceleration of the shuttlecock when t =0.75 s. (d) A model of the shuttlecock's velocity is Umar(1-e-kt). Use the table to suggest an appropriate value for 'mar, the terminal velocity. Hint: What is lim Uma(-)? (e) Plot the points and the curve to verify that they are in good agreement when k 3. (f) Use the equation in (d) to calculate the acceleration whent 0.75s (g) Use the eqation in (d) to calculate the total distance travelled between 0 and 2 seconds

Answer 1

Total ditamce ave lled Riemann naw. ← Hence tota dintance travelled 1ΛΣ Vídt 2. a^ppxei mate t05 5.0A.

ere we have med Matlabㅢσ plot the data Omd madel g- atol dirtomce. trcavellhd i model V dt- Bt 2

%%Matlab code for plotting the data and model clear all close all all data tt=0:0.25:2.0; vv [0 3.3 4.8 5.5 5.9 6.1 6.1 6.1 6.1]; model for velocity v-e (t) 6.1.(1-exp(-3*t)); plotting the data hold orn plot (tt, vv, 'r*", linewidth',2) plot (tt, v(tt)) xlabel('time in sec') ylabel'Velocity in m/sec') title( 'Time vs. Velocity plot') legend 'Actual data', 'Model data') box on grid on 88888888응888888 End of Code 888888888888 Time vs. Velocity plot ● Actual data Model data 드 1.2 0.4 1.6 18 02 06 0.8 1.4 time in sec Published with MATLABE R2018a

%%Matlab code for plotting the data and model
clear all
close all

%all data
tt=0:0.25:2.0;
vv=[0 3.3 4.8 5.5 5.9 6.1 6.1 6.1 6.1];

%model for velocity
v=@(t) 6.1.*(1-exp(-3*t));

%plotting the data
hold on
plot(tt,vv,'r*','linewidth',2)
plot(tt,v(tt))
xlabel('time in sec')
ylabel('Velocity in m/sec')
title('Time vs. Velocity plot')
legend('Actual data','Model data')
box on
grid on
%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%