Posted by **James** on Tuesday, August 23, 2011 at 5:22am.

Sam kicks a ball horizontally along a deck that is 5 m

above the ground.

The ball goes off the edge of the deck.

A model for the path of the ball once it leaves the deck is a parabola.

The equation of the parabola is y = ax^2+ bx + c.

The ball hits the ground at a horizontal distance of 3.1 m from the edge of the deck.

Find the values of a, b and c.

SHOW WORKING. STEP BY STEP

- math -
**drwls**, Tuesday, August 23, 2011 at 6:28am
If y is the height above the ground,

y = 5 when x = 0, so

a*0^2 + b*0 + c = 5,

so c = 5

When x = 0, the slope of the trajectory (path) is zero, so

dy/dx = 2ax + b = 0 at x = 0, so b = 0

When x = 3.1, y = 0, so

a(3.1)^2 +5 = 0

a = -5/(3.1)^2 = -0.521

y = -0.521 x^2 + 5

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