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?Select one of the options below as your answer: A. 18.3 meters/second B. 43.3 meters/second C. 25.0 meters/second D. 28.9 meters/second E. 32.1 meters/second
v =s/t =500/10 =50 m/s.
v(y) = v•sinα = 50•sin30º = 25 m/s
C. 25.0 meters/second
To find the vertical velocity of the motion, we can use the following equation:
Vertical velocity (Vv) = Velocity (V) * sin(θ),
where
- Velocity (V) is the constant speed of the bicyclist, and
- θ is the angle of the incline (30.0° downward from the horizontal).
Since the question does not provide the velocity, we need to calculate it first.
Given:
- Distance travelled (d) = 500 meters, and
- Time taken (t) = 10.0 seconds.
We can calculate the velocity using the equation:
Velocity (V) = Distance (d) / Time (t).
Let's substitute the given values:
Velocity (V) = 500 meters / 10.0 seconds = 50 meters/second.
Now, we can substitute this value into the equation for vertical velocity:
Vertical velocity (Vv) = 50 meters/second * sin(30.0°).
Using a calculator, sin(30.0°) ≈ 0.5.
Vertical velocity (Vv) = 50 meters/second * 0.5 = 25 meters/second.
Therefore, the vertical velocity of this motion is 25.0 meters/second.
So, the answer is C. 25.0 meters/second.
To find the vertical velocity of the motion, we need to understand the components of the velocity vector. The vertical velocity can be found using the equation:
Vertical Velocity = Velocity * sin(θ)
where
Velocity = distance / time (since the bicyclist is moving at a constant speed)
First, let's calculate the velocity. We are given that the bicyclist takes 10.0 seconds to travel 500 meters. Therefore,
Velocity = 500 meters / 10.0 seconds = 50.0 meters/second
Next, we need to find the sine of the angle θ. The path is inclined 30.0° downward, which means the angle is negative relative to the horizontal. Since sin(-θ) = -sin(θ), we can use the positive value of the angle (30.0°) for our calculations:
Vertical Velocity = 50.0 meters/second * sin(30.0°)
Now, let's calculate sin(30.0°):
sin(30.0°) = 0.5
Substituting this into the equation:
Vertical Velocity = 50.0 meters/second * 0.5 = 25.0 meters/second
Therefore, the vertical velocity of this motion is 25.0 meters/second.
The correct answer is C. 25.0 meters/second.