Question: At time t, a projectile launched with angle of elevation α and initial velocity v0 has position x(t)=(v0 cos α)t and y(t)=(v0 sin α)t - ½ gt2, where g is the acceleration due to gravity.
(a) A football player kicks a ball at an angle of 36° above the ground with an initial velocity of 60 feet per second. Write the parametric equations for the position of the football at time t seconds. Use g = 32 ft/sec2.
(b) Graph the path that the football follows.
(c) How long does it take for the football to hit the ground? How far is it from the spot where the football player kicked it?
(d) What is the maximum height the football reaches during its flight?
(e) At what speed is the football traveling 1 second after it was kicked?