An object is propelled upward at an angle θ, 45° < θ < 90°, to the horizontal with an initial velocity of υ0 feet per second from the base of a plane that makes an angle of 45°with the horizontal. See the illustration. If air resistance is ignored, the distance R that it travels up the inclined plane is given by the function
(a) Show that
(b) In calculus, you will be asked to find the angle θ that maximizes R by solving the equation
sin(2θ) + cos(2θ) = 0
Solve this equation for u.
(c) What is the maximum distance R if υ0 = 32 feet per second?
(d) Graph R = R(θ), 45° ≤ θ ≤ 90°, and find the angle θ that maximizes the distance R. Also find the maximum distance. Use υ0 = 32 feet per second. Compare the results with the answers found earlier.
