Question

50 PTS

Please answer the following and include your work:
Suppose a Ford Taurus is passing under an overpass. The height of the overpass is 17 feet (5.2 meters) above the road. At what minimum distance would the driver of the Taurus be able to see a vehicle at the top of the overpass using their rearview mirror. Suppose that the mirror is at the maximum angle permitted to see out the back window.

Extra (if you aren't tired of answering the first): Also calculate the angle and distance of the vehicle for an overpass height of 15 feet. And further calculate the distance with a mirror that is at the normal angle at both overpass heights.

Answer 1

The driver of the Taurus would be able to see a vehicle on top of a 15-foot overpass at a minimum distance of 112.5 feet.

Step-by-step explanation:

To solve this problem, we need to use the concept of similar triangles. Let's assume that the Ford Taurus is a point, and draw a right triangle representing the Taurus, the overpass, and the vehicle on top of the overpass, as shown below:

* vehicle

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|

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---------+------- overpass

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|

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T rearview mirror

Let's use h to represent the height of the vehicle on top of the overpass, and d to represent the minimum distance at which the driver can see the vehicle in the rearview mirror. Using similar triangles, we have:

h / d = 17 / (d + L)

where L is the horizontal distance from the Taurus to the base of the overpass. We can solve for d by cross-multiplying and simplifying:

h(d + L) = 17d

hd + hL = 17d

d = hL / (17 - h)

Now, let's substitute h = 17 feet and L = 15 feet (assuming the Taurus is in the middle of the lane), and calculate d:

d = 17 * 15 / (17 - 15) = 255 / 2 = 127.5 feet

Therefore, the driver of the Taurus would be able to see a vehicle on top of a 17-foot overpass at a minimum distance of 127.5 feet.

For a 15-foot overpass, we can repeat the calculation with h = 15 feet:

d = 15 * 15 / (17 - 15) = 225 / 2 = 112.5 feet

Therefore, the driver of the Taurus would be able to see a vehicle on top of a 15-foot overpass at a minimum distance of 112.5 feet.