Apply Netwon’s Divided Difference interpolation of the velocity, find the distance covered by the rocket from � = 5s to � = 16s.

Provide complete solutions to the following problems. The completed assignments must be prepared in strict accordance with the format and guidelines specified in the Homework Assignment Submission Guidelines. Not following the guidelines in a perfect manner will result in loss of LOTS OF CREDIT. The guidelines will be strictly enforced. Problem 1: You are given data for the upward velocity of a rocket as a function of time in Table 1 below. Apply the third-order Lagrange interpolation to estimate the acceleration at � = 9.5s. Calculate the true error of your estimation, if the data given in the table was derived from the formula �(�) = 2000 ln [ 14 × 104 14 × 104 − 2100� ] − 9.8�, 0 ≤ � ≤ 30 Problem 2: #2 in Ch 05.05 Table 1 Given Velocity and Time Data for a Rocket

Provide complete solutions to the following problems. The completed assignments must be prepared in strict accordance with the format and guidelines specified in the Homework Assignment Submission Guidelines. Not following the guidelines in a perfect manner will result in loss of LOTS OF CREDIT. The guidelines will be strictly enforced. Problem 1: #5 in Ch 05.02 Problem Set Problem 2: You are given data for the upward velocity of a rocket as a function of time in Table 1 below. Apply the direct interpolation method, use quadratic interpolant approximation of the velocity to find the acceleration at � = 16s. Problem 3: You are given data for the upward velocity of a rocket as a function of time in Table 1 below. Apply Netwon’s Divided Difference interpolation of the velocity, find the distance covered by the rocket from � = 5s to � = 16s.