The path of a projectile that is launched h feet above the ground with an initial velocity of t\) feet per second and at an angle 0 with the horizontal is given by the parametric equations
where t is the time, in seconds, after the projectile was launched. The parametric equation for x gives the projectile’s horizontal distance, in feet. The parametric equation for y gives the projectile’s| height, in feet. Use these parametric equations to solve Exercises 69 -70.
The figure shows the path for a baseball that was hit with an initial velocity of 150 feet per second at an angle of 35° to the horizontal. The ball was hit at a height of 3 feet off the ground.
a. Find the parametric equations that describe the position of the ball as a function of time.
b. Describe the ball's position after 1, 2, and 3 seconds. Round to the nearest tenth of a foot. Locate your solutions on the plane curve.
c. How long is the ball in flight? (Round to the nearest tenth of a second. ) What is the total horizontal distance that it travels, to the nearest tenth of a foot, before it lands? Is your answer consistent with the figure shown?
d. Use the graph to describe something about the path of the baseball that might be of interest to the player who hit the ball. Then verify your observation algebraically.
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