SOLUTION: A golf ball is hit and flies a horizontal distance of 180 m reaching a maximum height of 30 m. a. Draw a sketch of the function and find the equation of its height (h) as a fun

Question 1027397: A golf ball is hit and flies a horizontal distance of 180 m reaching a maximum height of 30 m.
a. Draw a sketch of the function and find the equation of its height (h) as a function of the horizontal distance (d) that it has travelled.
b. What is the height of the ball after its travelled 25 m horizontally (2 decimal places)?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A golf ball is hit and flies a horizontal distance of 180 m reaching a maximum height of 30 m.
a. Draw a sketch of the function and find the equation of its height (h) as a function of the horizontal distance (d) that it has travelled.
=================
Use graph paper.
Plot the points (0,0) and (180,0), the start and end of the flight.
Add the point (90,30).
Draw an approximation of a parabola thru the 3 points.
----
To find the function:
You have 3 points listed above.
It'll be y = ax^2 + bx + c
Sub the x & y for each point.
0 = a*0 + b*0 + c -- > c = 0
---
30 = a*90^2 + 90b
8100a + 90b = 30
270a + 3b = 1 Eqn A
---
0 = a*180^2 + 180b
180a + b = 0
540a + 3b = 0
270a + 3b = 1 Eqn A
------------------------------ Subtract
270a = -1
a = -1/270
b = -180a = 2/3
--> y = -x^2/270 + 2x/3
-------
b. What is the height of the ball after its travelled 25 m horizontally (2 decimal places)?
Estimate the y value at x = 25.

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