SOLUTION: A soccer ball is kicked from the goal crease. The ball travels along the path modelled by the equation {{{h=-.05d^2+3d}}}, where h is the height of the ball in meters and d is the

Question 1032520: A soccer ball is kicked from the goal crease. The ball travels along the path modelled by the equation , where h is the height of the ball in meters and d is the horizontal distance in meters.
a) How far does the ball travel horizontally?
My answer:
d = 6
The ball travels 6m before returning to the ground
b) If a 1.85 m tall soccer player stands 40 m away from the goalkeeper, how far over his head will the ball travel?
c) What is the maximum height the ball will travel to?
Thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A soccer ball is kicked from the goal crease. The ball travels along the path modelled by the equation h=-.05d^2+3d, where h is the height of the ball in meters and d is the horizontal distance in meters.
a) How far does the ball travel horizontally?
The height is zero when the ball hits the ground.
Solve
-0.05d^2 + 3d = 0
Factor:
-d(0.05d - 3) = 0
0.05d - 3 = 0
0.05d = 3
d = 300/5 = 60 meters
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b) If a 1.85m tall soccer player stands 40m away from the goalkeeper, how far over his head will the ball travel?
Question:: From what point was the ball kicked?
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c) What is the maximum height the ball will travel to?
Max occurs when d = -b/(2a) = -3/(2*0.05) = 30
h(30) = -0.05(30)^3 + 3(30) = -45+90 = 45 ft (maximum height)
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Cheers,
Stan H.
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