A Martian rover is moving up a hill sloped at 30.0° with the horizontal. If it has a constant velocity of 1.50 meters/second, calculate its vertical displacement after 21.0 seconds.
D = Vo*t = 1.5 * 21 = 31.5 m. @ 30 Deg.
Dy = 31.5*sin30 = 15.75 m.
To calculate the vertical displacement of the Martian rover, we need to find the component of its velocity that is parallel to the hill, which will give us its vertical velocity.
First, let's find the vertical component of the velocity:
Vertical velocity = velocity * sin(θ)
where θ is the angle of the hill (30.0° in this case).
Vertical velocity = 1.50 m/s * sin(30.0°)
Vertical velocity ≈ 1.50 m/s * 0.5
Vertical velocity ≈ 0.75 m/s
Now, we can calculate the vertical displacement using the formula:
Vertical displacement = vertical velocity * time
Vertical displacement = 0.75 m/s * 21.0 s
Vertical displacement ≈ 15.75 meters
Therefore, the vertical displacement of the Martian rover after 21.0 seconds is approximately 15.75 meters.
To calculate the vertical displacement, we need to find the component of the velocity vector that is perpendicular to the slope. This component is given by the formula:
Vertical component = Velocity * sin(angle)
where the angle is measured in radians. Here, the angle is 30.0°, which is approximately 0.5236 radians.
So, the vertical component of the velocity is:
Vertical component = 1.50 m/s * sin(0.5236) = 1.50 m/s * 0.5 = 0.75 m/s
Now, we can calculate the vertical displacement by multiplying the vertical component of the velocity by time:
Vertical displacement = Vertical component * time
Given that the time is 21.0 seconds, the vertical displacement is:
Vertical displacement = 0.75 m/s * 21.0 s = 15.75 meters
Therefore, the vertical displacement of the Martian rover after 21.0 seconds is 15.75 meters.