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?
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