If a 2000 pound train tilts of a 20 foot cliff at a 135 angle how long will it take to reach the ground?
To determine how long it will take for the train to reach the ground, we can use the principles of physics. Specifically, we can use the equations of motion under constant acceleration.
To solve this problem, we need to break it down into two components: the horizontal (x) and vertical (y) motions of the train.
First, let's focus on the vertical motion. We know that the train starts from rest at the top of the cliff and accelerates due to gravity (approximately 9.8 m/s²). The train will continue to accelerate until it reaches the ground.
To find the time it takes for the train to reach the bottom (t), we can use the kinematic equation:
y = v₀t + (1/2)gt²
where:
- y is the vertical distance traveled (20 feet = 6.1 meters),
- v₀ is the initial vertical velocity (0 m/s),
- g is the acceleration due to gravity (9.8 m/s²), and
- t is the time.
Since the train starts from rest, the initial vertical velocity is zero. The equation simplifies to:
y = (1/2)gt²
Rearranging the equation to solve for time (t), we get:
t² = (2y) / g
t = √((2y) / g)
Substituting the given values:
t = √((2 * 6.1) / 9.8) ≈ √(12.2 / 9.8) ≈ √1.244 ≈ 1.115 seconds
Therefore, it will take approximately 1.115 seconds for the 2000 pound train to reach the ground from the 20-foot cliff at a 135-degree angle.