When you look into your car's 5.0-cm-tall rear-view mirror fro...

Question

When you look into your car's 5.0-cm-tall rear-view mirror from 35 cm away, the front of a bus, from the ground to the roof, exactly fills the mirror. If the bus is 17 m from the mirror, how tall is the bus?

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A person in a park uses a 4.0 centimeter tall flat mirror which he holds 30 centimeters away from his eyes through the mirror. He observes a tree in the distance. The tree fills the mirror view from its base to its top. If the tree is 15 m from the mirror, what is the tree's height? So that is our end goal. So our end goal is to figure out what the height of this tree is considering the following conditions put together in this problem. So using all these tidbits of information that are provided to us, we need to use that information to help us solve for the tree's height. And that is our end goal. Awesome. We're also given some multiple choice answers. Let's read them off to see what our final answer might be. But let's quickly note first that all the units are in meters. So A is 2.5 B is 1.0 C is 2.0 and D is 1.7. So first off, let us consider that the distance between the person's eyes and the mirror is 30 centimeters. Therefore, the light travels a distance of 30 centimeters and spreads from an initial height close to zero and extends up to 4.0 centimeters beyond the mirror, the light rays continue to diverge at the same rate. So now at this point, let us create a diagram to help us better visualize this problem. And the type of diagram we're gonna create is a ray model of light. So I've gone ahead and found a detailed diagram for us to use to help us visualize this problem. So as you can see, we have our stick figure which represents our person which is standing 15 m away from a tree which we have our tree drawn here. And we're trying to find the height of the tree. And that value is H subscript two and H subscript one represents the height of our person standing in the park and there's a distance of 0.3 m away from the person and where the light rays diverge, that's where those dotted lines represent is the angle for where the, where the rays diverge. And we also have this little curved, you know, angle looking thing which represents our mirror, which the mirror is 30 centimeters away from the person's eyes, which they've gone ahead in this diagram, we've gone ahead and converted centimeters to meters. So it's 0.3 m. And our s one value represents from where our person is standing to where the mirror is located. And our S two value is where are the light rays are diverging? Or I should say the light. Yeah, where the light rays are diverging to where the tree is located. Awesome. So now that we have a handy dandy diagram to help us visualize the geometry principles that are in place here. And what exactly is going on in this problem? We need to write down all of our known and unknown variables to help us solve for our final answer. So let's go ahead and write down all of our variables. So we know that H one is given to us in the problem itself as 4.0 centimeters which is equal to 0.04 m. We also know the value of S one which is equal to 30 centimeters, which is equal to zero point 3 0 m. OK. We also know the value for S two because it's 15 m plus 0.30 m which is equal to 15.3 m. And we do not know what H two is. That is the value that we're trying to find. We do not know what the height of the tree is awesome. So now we can apply the geometry that is found in our diagram to recall and use the following equation that the height of the tree H two is equal to S two divided by S one, all multiplied by H one. So now we can plug in our known variables and solve for H two, the height of our tree which is equal to 15.3 m divided by 0.30 m multiplied by 0.04 meters. Which when we plug that into a calculator, we will get 2.04 m which is approximately equal to 2.0 m. Because as you can see all of our multiple choice answers are rounded to one decimal place. So that means we can just leave our answer as 2.0 m. Therefore, the height of the tree is 2.0 m tall. And that is our final answer. Hooray, we did it. So looking at our multiple choice answers, the correct answer that corresponds to our answer is the letter C 2.0 m. So before I close up the video here and say goodbye, if you're wondering why in the world we didn't stick with centimeters instead for our answer to keep things easy. Why do we have to do conversions? It's because all of our multiple choice answers as you can tell were in meters. So that's why we had to convert centimeters to meters. And we have to keep all of our units consistent in order to get the correct answer So this problem is fairly easy. As long as you have an understanding of geometry principles and how to apply them and manipulate them to solve for whatever variable you're trying to find. Well, that's it. Well, thank you so much for watching everybody. I hope to see you in the next video. I hope that helped and thank you so much for watching. Bye.

When you look into your car's 5.0-cm-tall rear-view mirror from 35 cm away, the front of a bus, from the ground to the roof, exactly fills the mirror. If the bus is 17 m from the mirror, how tall is the bus?

Key Concepts

Similar Triangles

Proportional Relationships

Distance and Magnification

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