SOLUTION: A javelin is thrown from a height of 2m above the ground. It lands 60 meters away. The path of the javelin can be represented by the equation {{{ y=ax^2+bx+c }}} a) What does

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A javelin is thrown from a height of 2m above the ground. It lands 60 meters away. The path of the javelin can be represented by the equation {{{ y=ax^2+bx+c }}} a) What does       Log On


   



Question 993370: A javelin is thrown from a height of 2m above the ground.
It lands 60 meters away. The path of the javelin can be represented by the equation +y=ax%5E2%2Bbx%2Bc+
a) What does x and y represent in this situation?
b)If it is known that the point (10,15) lies on the path given by the equation +y=ax%5E2%2Bbx%2Bc+, use algebra and all the information given in a) and b) to show
that:
+a=-2%2F75+ , +b=47%2F30+ and c = 2
c)Hence find the height of the javelin after travelling 20m horizontally
For a) Does y represent the height of the javelin, and x represent the horizontal distance traveled?
For b) I have no idea :c
For c) Really stuck!
It would be very helpful if you could draw up a graph too!! Thanks for help!!

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a) What does x and y represent in this situation?
y represent height (dependent variable,depends on how x changes )
x represent the path (dependent variable,it is a variable that stands alone and isn't changed by the other variables you are trying to measure )
b)
If it is known that the point (10,15) lies on the path given by the equation y=ax%5E2%2Bbx%2Bc, use algebra and all the information given in a) and b) to show that:
a+=+-2%2F75, b+=+47%2F30 and c+=+2
if the point (x,y)=(10,15), we have
y=ax%5E2%2Bbx%2Bc
15=100a%2B10b%2Bc ..............eq.1
if a+=+-2%2F75, b+=+47%2F30 and c+=+2, we have equation like this:
y=-%282%2F75%29x%5E2%2B%2847%2F30%29x%2B2+...now,show that y=15 when x=10

y=+-%282%2F75%2910%5E2%2B%2847%2F30%2910%2B2+
y=+-%282%2F75%29100%2B%2847%2F30%2910%2B2+
y=+-%282%2F15%2920%2B%2847%2F3%29%2B2+
y=+-%2840%2F15%29%2B%2847%2F3%29%2B2+
y=+-%2840%2F15%29%2B%28%2847%2A5%29%2F15%29%2B%282%2A15%29%2F15+
y=+%28-40%2B235%2B30%29%2F15

y=+225%2F15

y=+15+

c)
Hence find the height y of the javelin after traveling x=20m horizontally
y=+-%282%2F75%29x%5E2%2B%2847%2F30%29x%2B2

y=+-%282%2F75%2920%5E2%2B%2847%2F30%2920%2B2+
y=+-%282%2F75%29400%2B%2847%2A20%29%2F30%2B2
y=+-%28800%2F75%29%2B%28940%29%2F30%2B2
y=+-%28160%2F15%29%2B%28470%2F15%29%2B30%2F15
y=+%28470-160%2B30%29%2F15%29
y=+%28500-160%29%2F15%29
y=+340%2F15%29
y=22.66666666666667
y=22.7