Question 1176636: A golfer attempts to hit a golfball from a platform above the ground. The function that models the height of the ball is: y= -5t^2-40t+100 where y represents the height, in meters, above the ground at the time, t seconds after contact. There are power lines 185m above the ground. Will the golfball hit the power lines? Be clear and concise in your explanation with reference to you worked solution.
Found 2 solutions by Boreal, ankor@dixie-net.com:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! set the equation equal to 185, BUT the middle term is the speed of the golfball off the club, and that can't be negative. I will call it +40t
so
y=-5t^2-40t+100=185
-5t^2+40t-85=0
divide by -5
t^2-8t+17=0
t=(1/2)(8+/- sqrt (64-68)); complex solution. No, it will not hit them.
vertex is at t=-8/-2 or 4 sec
y(4)=-80+160+100=180 m
The curve to the left with vertex at x=-4 is the equation given.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! There has to be an upward velocity of 40 m/s therefore it is +40t
:
A golfer attempts to hit a golf ball from a platform above the ground.
The function that models the height of the ball is: y= -5t^2+40t+100 where y represents the height, in meters, above the ground at the time, t seconds after contact.
There are power lines 185m above the ground.
Will the golf ball hit the power lines?
Be clear and concise in your explanation with reference to your worked solution.
:
Will the golf ball reach 185m is the question
-5t^2 + 40t + 100 = 185
-5t^2 + 40t + 100 - 185 = 0
-5t^2 + 40t - 85 = 0
using the quadratic formula a=-5, b=40, c=-85
we got "no real roots" so it won't quite reach 185 meters
Graphically, power line is green
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