A train travels at 3m/s and parallel and very near to the train is a wall the has a slope of 12degrees, the window you see this wall through is .9m high, 2m across, and when you look out you first see the top edge at the lower left of the window, moving towards the top right of the window, how long at 3m/s will it take for the edge of the wall to no longer be visible?
To find the time it takes for the edge of the wall to no longer be visible, we can break down the problem into two steps: finding the distance traveled by the edge of the wall and then calculating the time it takes.
Step 1: Finding the distance traveled by the edge of the wall
When the edge of the wall is no longer visible, it means the angle between the line of sight and the sloping wall is equal to the angle of elevation of the wall. This angle can be found using trigonometry.
Given:
- The height of the window: 0.9 m
- The width of the window: 2 m
- The slope of the wall: 12 degrees
To determine the distance traveled by the edge of the wall, we need to find the length of the side adjacent to the angle of 12 degrees in the triangle formed by the window.
Using the trigonometric relationship "tan(theta) = opposite/adjacent," we have:
tan(12 degrees) = 0.9 m / x
Solving for x:
x = 0.9 m / tan(12 degrees)
Step 2: Calculating the time it takes
Now, we need to calculate the time it takes to cover the distance x at a speed of 3 m/s.
Using the formula: time = distance / speed,
time = x / 3 m/s
Substituting the value of x from the previous step:
time = (0.9 m / tan(12 degrees)) / 3 m/s
Now you can calculate this expression to find the time it takes for the edge of the wall to no longer be visible.