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 θo (degrees) above horizontal. With the pictured imposed coordinate system, the parametric equations of the cyclist will be:
x(t) = 100t cos(θ)
y(t) = -16t2 + 100t sin(θ) + 10.
(These are the parametric equations for the motion of the stunt cyclist.)
(a) Calculate the horizontal velocity of the cyclist at time t; this is the function x'(t)=
(b) What is the horizontal velocity if θ = 20o?
(c) What is the horizontal velocity if θ = 45o? (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 θ = 20o? (Four decimal places.)
(f) What is the vertical velocity if θ = 45o? (Four decimal places.)
(g) The vertical velocity of the cyclist is zero at time 0 seconds.
(h) If the cyclist wants to have a maximum height of 35 feet above the landing zone, then the required launch angle is θ = ?. (Accurate to four decimal places.)