The path of a projectile that is launched h feet above the ground with an initial velocity of v0 feet per second and at an angle θ with the horizontal is given by the parametric equations x = (v0 cos θ)t and y = h + (v0 sin θ)t - 16t2,where t is the time, in seconds, after the projectile was launched.A football player throws a football with an initial velocity of100 feet per second at an angle of 40° to the horizontal. The ball leaves the player’s hand at a height of 6 feet.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.c. How long, to the nearest tenth of a second, is the ball in flight? What is the total horizontal distance that it travels before it lands?d. Graph the parametric equations in part (a) using a graphing utility. Use the graph to determine when the ball is at its maximum height. What is its maximum height?Round answers to the nearest tenth.
The path of a projectile that is launched h feet above the ground with an initial velocity of v0 feet per second and at an angle θ with the horizontal is given by the parametric equations x = (v0 cos θ)t and y = h + (v0 sin θ)t - 16t2,where t is the time, in seconds, after the projectile was launched.A football player throws a football with an initial velocity of100 feet per second at an angle of 40° to the horizontal. The ball leaves the player’s hand at a height of 6 feet.
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.
c. How long, to the nearest tenth of a second, is the ball in flight? What is the total horizontal distance that it travels before it lands?
d. Graph the parametric equations in part (a) using a graphing utility. Use the graph to determine when the ball is at its maximum height. What is its maximum height?Round answers to the nearest tenth.
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