A student has built a 20-cm-long pinhole camera for a science fair project. She wants to photograph the Washington Monument, which is 167 m (550 ft) tall, and to have the image on the film be 5.0 cm high.
Are not there two similar triangles here..from the pinhole enveloping the monument on one side, from the pinhole enveloping the image on the other.
Using similarity,
5cm/167m=.2m/d
solve for d, the distance to the Monument.
I think I did this problem in the 8th grade, it is odd seeing it again.
668m
To determine the necessary distance between the pinhole camera and the Washington Monument, we can use similar triangles. The height of the Washington Monument, the height of the image on the film, and the distance between the camera and the monument will form a triangle.
Let's start by setting up the proportion between the heights of the Washington Monument and the image on the film:
Height of Washington Monument / Height of Image on Film = Distance to Monument / Distance to Image on Film
Given:
Height of Washington Monument = 167 m
Height of Image on Film = 5.0 cm
Distance to Image on Film = 20 cm (provided in the problem)
Now, let's calculate the distance to the Washington Monument.
Distance to Monument = (Height of Washington Monument * Distance to Image on Film) / Height of Image on Film
Distance to Monument = (167 m * 20 cm) / 5.0 cm
First, let's convert the height of the Washington Monument to centimeters:
Height of Washington Monument = 167 m * 100 cm/m = 16,700 cm
Now, we can substitute the values:
Distance to Moment = (16,700 cm * 20 cm) / 5.0 cm
Distance to Monument = 334,000 cm / 5.0 cm
Finally, we can calculate the distance to the Washington Monument:
Distance to Monument = 66,800 cm
So, the student needs to place the pinhole camera approximately 66,800 cm (or 668 m) away from the Washington Monument in order to have the image on the film be 5.0 cm high.
To calculate how far the student will need to place the pinhole camera from the Washington Monument to achieve her desired image, we can use similar triangles.
First, let's set up the proportion using the height of the Washington Monument and the corresponding height on the film:
(Height of Monument) / (Distance to Monument) = (Height on Film) / (Distance to Film)
We know that the height of the Washington Monument is 167 m and the desired height on the film is 5.0 cm. We need to find the distance to the Monument.
Let's assume "x" represents the distance to the Monument. Now we can set up the proportion:
167 m / x = 5.0 cm / 20 cm
Since the heights are in different units (meters and centimeters), we need to convert one of them to the other unit. Let's convert 5.0 cm to meters:
5.0 cm = 5.0 cm * (1 m / 100 cm)
= 0.05 m
Now we can substitute the values into the proportion:
167 m / x = 0.05 m / 20 cm
To find "x," we can cross-multiply and solve for "x":
167 m * 20 cm = 0.05 m * x
3340 cm*m = 0.05 m * x
Now we can cancel out the units:
3340 = 0.05x
To isolate "x," divide both sides of the equation by 0.05:
x = 3340 / 0.05
x ≈ 66800
So, the student will need to place the pinhole camera approximately 66,800 meters away from the Washington Monument to achieve her desired image size of 5.0 cm on the film.