MHB Word problem: initial height of projectile

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The height of the cliff from which a ball is thrown is determined using the equation h = -5t^2 + 5t + 210. By substituting t = 0 into the equation, the initial height is calculated as h = 210 meters. The discussion confirms that the cliff's height is indeed 210 meters. Understanding the use of the equation is crucial for solving similar projectile motion problems. The correct interpretation of the initial conditions leads to the accurate conclusion about the cliff's height.
mathdrama
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A ball is thrown from a cliff. The path of the ball modeled by the equation
h = -5t^2+ 5t + 210,
where h is the height, in metres, of the ball above the ground, and t is the time, in seconds, after it is thrown. How high is the cliff?

Not really sure how to do this problem. I know that one of the roots is -6, but I don't know how to use this information.
 
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Re: word problem

mathdrama said:
A ball is thrown from a cliff. The path of the ball modeled by the equation
h = -5t^2+ 5t + 210,
where h is the height, in metres, of the ball above the ground, and t is the time, in seconds, after it is thrown. How high is the cliff?

Not really sure how to do this problem. I know that one of the roots is -6, but I don't know how to use this information.

Since $t$ is the time after the ball is thrown, you have to set $t=0$ at the equation to find the height of the ball before it's thrown, so when it is still on the cliff.
 
Re: word problem

So to make sure I have this right...

Let t = 0
h = -5(0^2) + 5(0) + 210
h = 0 + 0 + 210
h = 210
Therefore, the cliff is 210 meters high.
 
Re: word problem

mathdrama said:
So to make sure I have this right...

Let t = 0
h = -5(0^2) + 5(0) + 210
h = 0 + 0 + 210
h = 210
Therefore, the cliff is 210 meters high.

Yes, it is right! (Yes)
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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