Question 242538: the path of a golf ball hit at an angle of about 10 degrees to the horizontal can be modelled by the function h= -0.002dsquared + 0.4d
where h is the height of the ball, in metres, and d is the horizontal distance the ball travels, in metres, until it first hits the ground.
a. What is the maximum height reached by the ball?
b, What is the horizontal distance of the ball from the golfer when the ball reaches its maximum height?
c. What distance does the ball travel horizontally until it first hits the ground?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! h= -0.002d^2 + 0.4d
where h is the height of the ball, in metres, and d is the horizontal distance the ball travels, in metres, until it first hits the ground.
a. What is the maximum height reached by the ball?
h(d) = -0.002d^2 + 0.4d
-0.002d^2 + 0.4d - h = 0
The vertex is at -b/2a = -0.4/-0.004 = 100
h(100) = -0.002*10000 + 40
max = 20 meters
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b, What is the horizontal distance of the ball from the golfer when the ball reaches its maximum height?
d at the vertex = 100 meters
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c. What distance does the ball travel horizontally until it first hits the ground?
The equation is symmetrical, so it's 2x the distance at the vertex
= 200 meters
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