What Equation Models a Semi-Elliptical Arch Allowing a Ship to Pass Underneath?

[ZaTaisho]

Homework Statement

A bridge is to be constructed across a river that is 150 feet wide. The arch of the bridge is to be semi-elliptical and must be constructed so that a ship less than 50 feet wide and 40 feet high can pass safely through the arch, as shown in the figure.

(a) Find an equation for the arch. (Let x be the independent variable and y be the dependent variable. Assume the origin is at the surface of the river directly beneath the highest point of the arch.)

(b) Approximate the height of the arch in the middle of the bridge. (Round your answer to the nearest whole number.)

Homework Equations

x²/a² + y²/b² = 1

The Attempt at a Solution

I actually don't understand it.
As far as I know, the 150 needs to halved, thus making it:

x²/75² + y²/b² = 1

But I'm stuck from there...can anyone help?

 

[Dick]

Homework Statement

A bridge is to be constructed across a river that is 150 feet wide. The arch of the bridge is to be semi-elliptical and must be constructed so that a ship less than 50 feet wide and 40 feet high can pass safely through the arch, as shown in the figure.

(a) Find an equation for the arch. (Let x be the independent variable and y be the dependent variable. Assume the origin is at the surface of the river directly beneath the highest point of the arch.)

(b) Approximate the height of the arch in the middle of the bridge. (Round your answer to the nearest whole number.)

Homework Equations

x²/a² + y²/b² = 1

The Attempt at a Solution

I actually don't understand it.
As far as I know, the 150 needs to halved, thus making it:

x²/75² + y²/b² = 1

But I'm stuck from there...can anyone help?

Think in terms of xy coordinates with the origin they described. Can you name an (x,y) point that should be on the ellipse? Picture the ship just touching the ellipse.

 

[ZaTaisho]

Think in terms of xy coordinates with the origin they described. Can you name an (x,y) point that should be on the ellipse? Picture the ship just touching the ellipse.

I'm not entirely sure. I keep thinking of (25,0), but again I could most likely be wrong.
I do not understand material if they are just mathematically questioned upon me. I need examples, and the reason why. That is how I learn.

You can keep giving me questions all you want, but I'm not going to understand them, nor be able to figure them out. Questions just lead me into more confusion. I need guidance, not really assistance, because once I see how to do it, I am dependent upon myself to finish other related problems.

NOTE: I'm not trying to be mean or anything, I'm just stating on my learning style. If schools were giving me a hard time with these math terms, questions, and etc... then I don't see how questioning me will help either.

 

[symbolipoint]

ZaTaisho,

Try to DRAW the picture, and try to fit a cartesian coordinate system to it. You may then SEE the mathematical situation and solve the problem from this. Note that, you are actually given one of the points on the ellipse. This point comes in the form of the width and height of the ship.

 

[Dick]

I'm not entirely sure. I keep thinking of (25,0), but again I could most likely be wrong.
I do not understand material if they are just mathematically questioned upon me. I need examples, and the reason why. That is how I learn.

You can keep giving me questions all you want, but I'm not going to understand them, nor be able to figure them out. Questions just lead me into more confusion. I need guidance, not really assistance, because once I see how to do it, I am dependent upon myself to finish other related problems.

NOTE: I'm not trying to be mean or anything, I'm just stating on my learning style. If schools were giving me a hard time with these math terms, questions, and etc... then I don't see how questioning me will help either.

I'm asking you questions to try and figure out why you are having a hard time with the problem. And I'm not really asking you for an equation either. (25,0) is a point on the outside of the ship where it touches the water, right? I'm asking you for a point on the top of the ship where it would touch the bridge.