A bicyclist moving at a constant speed takes 10.0 seconds to travel 500 meters down a path inclined 30.0° downward from the horizontal. What is the vertical velocity of this motion?

To determine the vertical velocity of the motion, we need to break down the given information and solve step by step. Here's how we can do it:

1. The first step is to find the vertical displacement of the cyclist. Since the path is inclined downward at an angle of 30.0°, the vertical displacement (d) can be calculated using the formula:

d = distance * sin(angle)

where the distance is given as 500 meters, and the angle is 30.0°.

Plugging in the values:

d = 500 * sin(30.0°)
= 250 meters

So, the vertical displacement is 250 meters.

2. The next step is to find the time taken by the cyclist to complete the vertical displacement. Since the question states that the cyclist takes 10.0 seconds to travel the given distance (500 meters), we can assume the vertical displacement also took 10.0 seconds to complete.

3. Finally, we can calculate the vertical velocity (v) using the formula:

v = displacement / time

Plugging in the values:

v = 250 / 10.0
= 25 meters per second

Therefore, the vertical velocity of this motion is 25 meters per second.

To find the vertical velocity of the motion, we first need to calculate the vertical component of the displacement.

The path is inclined 30° downward from the horizontal, which means the vertical displacement is given by:

Vertical displacement = 500 meters * sin(30°)

Using the trigonometric identity sin(30°) = 0.5, we can substitute the value:

Vertical displacement = 500 meters * 0.5 = 250 meters

Since the motion takes place in 10.0 seconds, we can calculate the vertical velocity by dividing the vertical displacement by the time taken:

Vertical velocity = Vertical displacement / Time taken
= 250 meters / 10.0 seconds
= 25 meters/second

Therefore, the vertical velocity of this motion is 25 meters/second.

Vo = d/t = 500 / 10 = 50 m/s @ 30 Deg.

Yo = Vo*sinA = 50*sin30 = 25 m/s.