The height h(t) and horizontal distance s(t) traveled by a ball thrown at an angle q, with initial speed u, is given as: h(t) = u.t. sin(q) – 1 2 g.t 2 s(t) = u.t. cos(q) The acceleration due to...

The height h(t) and horizontal distance s(t) traveled by a ball thrown at an angle q, with initial speed u, is given as: h(t) = u.t. sin(q) – 1 2 g.t 2 s(t) = u.t. cos(q) The acceleration due to gravity is g = 9.81 m/sec.2 (a) Suppose the ball is thrown with a velocity u = 10 m/sec.2 at an angle of 35°. Use MATLAB to compute how high the ball will go, how far will it go, and how long will it take to hit the ground? (b) Use the values of u and q in part (a) above, to plot the ball’s trajectory, that is, plot h versus s for all positive values of h. (c) Plot the trajectories for the same value of u, but with different angles q: 20°, 30°, 45°, 60°, and 70°. Now find out for what angle the ball travels the highest? Mark this trajectory with bold faced line in your plot. (d) When a satellite orbits the earth, the satellite’s orbit forms an ellipse with earth located at one of the focal points of the ellipse. The satellite’s orbit can be expressed in terms of polar coordinates as: r = z / (1 - e cos q ) where, r and q are the distance and angle of the satellite from the center of the earth, z is a parameter specifying the size of the orbit, and e is the eccentricity of the orbit. A circular orbit has an eccentricity e equal to 0, whereas an elliptical orbit has an eccentricity between 0 ≤ e ≤ 1. If e > 1, the satellite follows a hyperbolic path and escapes from the earth’s gravitational field. Consider a satellite with a size parameter z = 1000 km. Plot the orbit of the satellite if (a) e = 0 (b) e = 0.25 and (c) e = 0.5. What is the closest distance of each of these orbits from earth? And how far is the farthest point on the orbit? Compare the result of all the three plots. What is the significance of the parameter z?