The path of a projectile that is launched h feet above the ground with an initial velocity of v 0 feet per second and at an angle θ with the horizontal is given by the parametric equations x = ( v 0 cos θ ) t and y=h+( v 0 sin θ ) t − 16 t 2 , where t is the time, in seconds, after the projectile was launched. A football player throws a football with an initial velocity of 100 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 afoot. 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 v 0 feet per second and at an angle θ with the horizontal is given by the parametric equations x = ( v 0 cos θ ) t and y=h+( v 0 sin θ ) t − 16 t 2 , where t is the time, in seconds, after the projectile was launched. A football player throws a football with an initial velocity of 100 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 afoot. 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.
Solution Summary: The author explains the parametric equations that show the position of the ball that is hit with the initial velocity, angle from the horizontal, and the height.
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
=
(
v
0
cos
θ
)
t
and y=h+(
v
0
sin
θ
)
t
−
16
t
2
,
where t is the time, in seconds, after the projectile was launched. A football player throws a football with an initial velocity of 100 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 afoot.
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?
Algebra and Trigonometry with Integrated Review and Worksheets Plus MyLab Math with eText -- Title-Specific Access Card Package, with Integrated Review (6th Edition)
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