A stunt cyclist needs to make a calculation for an upcoming cycle jump. The cyclist is traveling 100 ft/sec toward an inclined ramp which ends 10 feet above a level landing zone. Assume the cyclist maintains a constant speed up the ramp and the ramp is inclined A° (degrees) above horizontal. With the pictured imposed coordina system, the parametric equations of the cyclist will be: x(t) = 100t cos(A) y(t)=-16t² + 100t sin(A) + 10. (These are the parametric equations for the motion of the stunt cyclist.) y-axis 10 feet (a) Calculate the horizontal velocity of the cyclist at time t; this is the function x'(t)= (b) What is the horizontal velocity if A=20 degrees? (c) What is the horizontal velocity if A=45 degrees? (Four decimal places.) (d) Calculate the vertical velocity of the cyclist at time t; this is the function y'(t)= (e) What is the vertical velocity if A=20 degrees? (f) What is the vertical velocity if A=45 degrees? (Four decimal places.) (Four decimal places.) (g) The vertical velocity of the cyclist is zero at time seconds. (h) If the cyclist wants to have a maximum height of 35 feet above the landing zone, then the required launch angle is A= degrees. (Accurate to four decimal places.)