(20 pts) The height h(t) and velocity v(t) of a object thrown upward at any moment are given as follows. Where v0= initial velocity, = the initial angle with the horizontal plane and g= gravity of earth. Air resistance is neglected. Given the following parameter values; =50 degree, v0=10m/s and g=9.81m/s2, find the time t which minimizes the velocity using an initial interval of [0,3], a.)(3 pts) graphically, b.)(2 pts) analytically, c.) find the solution taking an initial =0.005 with the golden-section search method i. (4 pts) Perform two iterations by hand ii. (4 pts) Perform all iterations by Matlab algorithm d.) find the solution taking an initial tolerance tol =0.0001, and initial guess t0=0.5 with the Newton's method iii. (4 pts) Perform two iterations by hand iv. (3 pts) Perform all iterations by Matlab algorithm h(t)=y(t)=v0tsin0.5gt2 v(t)=v022v0gtsin+g2t2