A sled is moving at a constant speed down a surface inclined at 45.0° with the horizontal and travels 30 meters in 4 seconds. Calculate the vertical velocity of the sled at the end of 4 seconds.
it is moving at constant speed. that speed is 30m/4sec=7.5m/s
its final speed, still constant, is 7.5m/s.
This is a very odd question.
To calculate the vertical velocity of the sled at the end of 4 seconds, we need to break down the sled's motion into its horizontal and vertical components.
First, let's calculate the horizontal velocity of the sled. We know that the sled is moving at a constant speed, so the horizontal velocity remains constant. We can use the equation:
horizontal velocity = distance / time
Given that the sled travels 30 meters in 4 seconds, we can substitute these values into the equation:
horizontal velocity = 30 m / 4 s = 7.5 m/s
The horizontal velocity of the sled is 7.5 m/s.
Next, let's calculate the vertical velocity of the sled. We can use trigonometry to break down the sled's velocity into horizontal and vertical components. Since the surface is inclined at 45.0° with the horizontal, the vertical component of the velocity can be calculated using the equation:
vertical velocity = horizontal velocity * sin(angle)
Substituting the values we already know:
vertical velocity = 7.5 m/s * sin(45.0°)
Using a calculator, we find that sin(45.0°) = 0.7071. Substituting this value into the equation:
vertical velocity = 7.5 m/s * 0.7071 ≈ 5.30 m/s
Therefore, the vertical velocity of the sled at the end of 4 seconds is approximately 5.30 m/s.