Calculate numerically the maximum and minimum values that the height y(t) velocity v(t) z and acceleration a(t) of a ball with a mass of m = 0.5kg thrown vertically upward direction. (20 points) The ball moves under air resistance proportional to the square of its speed, with a resistance coefficient given as c_{u} = (21) / 1000 * (kg / m) It starts from position y(0) = 0 with an initial velocity of v(0) = 105m / s The gravitational acceleration is taken as g = 9.81m / (s ²) The equations of motion for the ball are given below:
d/dt (v) = - g - cd/m v/v (1)
d/dt (y) = v(2)
Equation (1) shows the velocity-dependent change in acceleration and can be solved using the first-order forward finite difference method. The velocity values obtained here can then be used in numerical integration (trapezoidal method) to find the corresponding y values, as seen in Equation (2)