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.
The speed is constant. All you need is the vertical component.
(30/4) cos 45
To calculate the vertical velocity of the sled at the end of 4 seconds, we need to find the vertical component of its velocity.
First, we will determine the horizontal and vertical distances traveled by the sled in 4 seconds. We are given that the sled travels a total distance of 30 meters in 4 seconds. Since the sled is moving at a constant speed, we can assume that the horizontal distance traveled is equal to the total distance. Therefore, the horizontal distance traveled by the sled is also 30 meters.
To find the vertical distance traveled by the sled, we can use trigonometry. The surface is inclined at an angle of 45.0° with the horizontal. The vertical distance traveled is equal to the horizontal distance multiplied by the sine of the angle. Therefore, the vertical distance traveled by the sled is 30 meters × sin(45.0°) = 21.2 meters.
Now that we have both the horizontal and vertical distances traveled, we can calculate the vertical velocity of the sled at the end of 4 seconds using the formula:
Vertical velocity = Vertical distance / Time
Vertical velocity = 21.2 meters / 4 seconds ≈ 5.3 meters/second
Therefore, the vertical velocity of the sled at the end of 4 seconds is approximately 5.3 meters/second.