You are on a train that is traveling at 3.0 m/s along a level straight track. Very near and parallel to the track is a wall that slopes upward at a 12° angle with the horizontal. As you face the window (0.86 m high, 2.0 m wide) in your compartment, the train is moving to the left, as the drawing indicates. The top edge of the wall first appears at window corner A and eventually disappears at window corner B. How much time passes between appearance and disappearance of the upper edge of the wall?

Question

You are on a train that is traveling at 3.0 m/s along a level straight track. Very near and parallel to the track is a wall that slopes upward at a 12° angle with the horizontal. As you face the window (0.86 m high, 2.0 m wide) in your compartment, the train is moving to the left, as the drawing indicates. The top edge of the wall first appears at window corner A and eventually disappears at window corner B. How much time passes between appearance and disappearance of the upper edge of the wall?

1 . s

Answer 1

To determine the time that passes between the appearance and disappearance of the upper edge of the wall, we can use basic trigonometry and the concept of relative velocity.

First, let's consider the horizontal distance covered by the train during this time interval. The width of the window (2.0 m) represents this horizontal distance. We know that the train is traveling at a speed of 3.0 m/s. Therefore, the time it takes to cover the width of the window is:

Time = Distance / Speed
Time = 2.0 m / 3.0 m/s
Time = 0.67 seconds

Now, let's determine the vertical distance covered by the upper edge of the wall during this time interval. To do this, we need to calculate the height of the wall that corresponds with the width of the window.

Since the wall is sloping upward at a 12° angle with the horizontal, the height of the wall can be calculated using trigonometry. We can use the tangent function, which is defined as the ratio of the opposite side (height of the wall) to the adjacent side (width of the window).

Tangent(12°) = Height of the wall / Width of the window
Height of the wall = Width of the window * Tangent(12°)
Height of the wall = 2.0 m * tan(12°)
Height of the wall ≈ 0.42 m

Now that we know the height of the wall, we can calculate the time it takes for the upper edge of the wall to move from corner A to corner B.

Time = Vertical distance / Vertical speed
Time = Height of the wall / Speed
Time = 0.42 m / 3.0 m/s
Time ≈ 0.14 seconds

Therefore, the time that passes between the appearance and disappearance of the upper edge of the wall is approximately 0.14 seconds.