A train moving at a constant speed on a surface inclined upward at 10.0° with the horizontal travels a distance of 400 meters in 5 seconds. Calculate the vertical velocity component of the train during this time period.
Goes up distance 400 sin 10 = 69.5 m
69.5 m/ 5 s = 13.9 m/s up
To calculate the vertical velocity component of the train, we can break down the velocity into horizontal and vertical components.
Given:
Distance traveled by the train = 400 meters
Time taken = 5 seconds
Angle of inclination = 10.0°
Step 1: Calculate the horizontal distance covered by the train.
The horizontal distance traveled can be calculated using the formula:
Horizontal distance = Distance * cos(angle)
Horizontal distance = 400 * cos(10.0°)
Step 2: Calculate the vertical distance covered by the train.
The vertical distance traveled can be calculated using the formula:
Vertical distance = Distance * sin(angle)
Vertical distance = 400 * sin(10.0°)
Step 3: Calculate the horizontal velocity component.
The horizontal velocity can be calculated using the formula:
Horizontal velocity = Horizontal distance / Time taken
Step 4: Calculate the vertical velocity component.
The vertical velocity can be calculated using the formula:
Vertical velocity = Vertical distance / Time taken
Now let's calculate the values:
Step 1: Calculate the horizontal distance
Horizontal distance = 400 * cos(10.0°)
Horizontal distance ≈ 400 * 0.9848
Horizontal distance ≈ 393.92 meters (rounded to 2 decimal places)
Step 2: Calculate the vertical distance
Vertical distance = 400 * sin(10.0°)
Vertical distance ≈ 400 * 0.1736
Vertical distance ≈ 69.44 meters (rounded to 2 decimal places)
Step 3: Calculate the horizontal velocity component
Horizontal velocity = Horizontal distance / Time taken
Horizontal velocity ≈ 393.92 / 5
Horizontal velocity ≈ 78.784 m/s (rounded to 3 decimal places)
Step 4: Calculate the vertical velocity component
Vertical velocity = Vertical distance / Time taken
Vertical velocity ≈ 69.44 / 5
Vertical velocity ≈ 13.888 m/s (rounded to 3 decimal places)
Therefore, the vertical velocity component of the train during this time period is approximately 13.888 m/s.
To calculate the vertical velocity component of the train, we need to find the train's velocity in the vertical direction.
First, let's calculate the train's velocity in the horizontal direction. Since the train is moving at a constant speed, the horizontal velocity remains constant throughout the motion. We can use the equation:
horizontal velocity = distance / time
The given information states that the train travels a distance of 400 meters in 5 seconds. Plugging those values into the equation, we can find the horizontal velocity:
horizontal velocity = 400 m / 5 s = 80 m/s
Now, we need to find the vertical velocity component. Since the train is moving on an inclined surface, the vertical velocity component is affected by the angle of inclination. The vertical velocity component can be calculated using:
vertical velocity = horizontal velocity * tangent(angle of inclination)
The angle of inclination is given as 10.0°. To calculate the tangent of the angle, we can use a scientific calculator. Taking the tangent of 10.0° gives us approximately 0.1763.
Finally, we can substitute the values into the equation to find the vertical velocity component:
vertical velocity = 80 m/s * 0.1763 ≈ 14.10 m/s
Therefore, the vertical velocity component of the train during this time period is approximately 14.10 m/s.