(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A ball is launched from a cliff 1 meter high. At the bottom of the cliff, the ground is not flat, it slants downward at a 45 degree angle as show. The ball's initial; velocity is 10 m/s and makes a 20 degree angle with the horizontal. Find x, the horizontal displacement of the ball from the edge of the cliff when it lands.

Ans: 24.85 m

Please see the picture that describes the problem in the attachments

2. Relevant equations

3. The attempt at a solution

When I tried solving this problem I got about 23.32 meters so I guess I'm doing something wrong.

What I did was solve for the equation that describes the position in the vertical direction as a function of time and got

y = -4.9*t^2 + 5t

I set this equal to negative one to find the time at which the ball was one meter below were it started (I set the coordinate system to be (0,0) were the ball originally starts), and got about 1.1916656. I then plugged this value into the equation that gives the displacement in the horizontal direction

x = 5sqrt(3)*t

x = 5sqrt(3)*1.1916656

x is about 10.32012682

I then solved for how far below the ground was from this point using trigonometry were

10.32012682 tan(pi/4) = 10.32012682, 10.32012682 = 10.32012682

from this I concluded that the point directly below the ball when the ball is exactly one meter below the point from were it started can be represented by the point (10.32012682,-11.32012682)

I then concluded that the equation that can describe the vertical position of the ground were it's slanted can be represented by the equation y(x)=-x-1

I then got rid of the parameter t in my equation that describes the vertical position of the ball by solving my equation that represents the horizontal position of the ball for t

x(t) = 5sqrt(3)t

t = x/(5sqrt(3))

y(t) = -4.9*t^2+5t

y(x) = (-4.9x^2)/25.3 + (5x)/(5sqrt(3)) = -(49x^2)/750 + (sqrt(3)x)3

I then set my equation that describes the height of the ball as a function of horizontal location to the equation that represents the height of the ground as a function of horizontal location

y = -(49x^2)/750 + (sqrt(3)x)3

y = - x - 1

-(49x^2)/750 + (sqrt(3)x)3 = - x - 1

I got that x is about 24.76 which is off from the answer on the sheet by about .9. Am I doing something wrong?

Thanks for any help anyone can provide me!

The picture

http://img36.imageshack.us/img36/8817/bookscanstation20110918.jpg [Broken]

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