Time, t (sec) 10 15 20 22.5 30 Velocity, v(m/s) 227.04 362.78 517.35 602.97 901.67 (a) Determine the value of the velocity at t = 16 seconds using third order Lagrangian polynomial to the nearest 3...

[C]  The upward velocity of a jet is given as a function of time as shown below:

Extracted text: Time, t (sec) 10 15 20 22.5 30 Velocity, v(m/s) 227.04 362.78 517.35 602.97 901.67 (a) Determine the value of the velocity at t = 16 seconds using third order Lagrangian polynomial to the nearest 3 significant figures. m/s. (b) Find the absolute relative approximate error for the third order polynomial approximation to the nearest 3 significant figures. percent. (c) Using the third order polynomial interpolant for velocity, find the distance covered by the jet from t = 11 seconds to t = 16 seconds to the nearest four significant figures. metres. (d) Using the third order polynomial interpolant for velocity, find the acceleration of the jet at t = 16 seconds to the nearest four significant figures. metres per square seconds.