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.
h=s•sinα=v•t•sinα=1.5•21•sin30=15.75 m
Well, well, well, looks like our Martian rover is on a hill-climbing adventure! Let's do some calculations to help it conquer that slope.
To find the vertical displacement of the rover, we need to break down its constant velocity into its horizontal and vertical components. Given that the slope is inclined at 30.0°, we can use some trigonometry to determine those components.
The vertical component, represented by Vy, can be found by multiplying the velocity by the sine of the angle:
Vy = 1.50 m/s * sin(30.0°)
And the horizontal component, represented by Vx, can be found by multiplying the velocity by the cosine of the angle:
Vx = 1.50 m/s * cos(30.0°)
Now that we have the horizontal and vertical components of velocity, we can determine the vertical displacement by multiplying the vertical component by time:
Vertical displacement = Vy * time
Vertical displacement = (1.50 m/s * sin(30.0°)) * 21.0 s
Now it's time to break out the calculator and crunch those numbers, my friend!
To calculate the vertical displacement of the Martian rover after 21.0 seconds, we need to find the component of the velocity vector in the vertical direction.
Given:
Slope angle (θ) = 30.0°
Velocity (v) = 1.50 m/s
Time (t) = 21.0 s
First, we need to find the vertical component of the velocity using trigonometry.
Vertical component of velocity = Velocity * sin(θ)
Vertical component of velocity = 1.50 m/s * sin(30.0°)
Vertical component of velocity = 1.50 m/s * 0.5
Vertical component of velocity = 0.75 m/s
Now, we can calculate the vertical displacement by multiplying the vertical component of velocity by time:
Vertical displacement = Vertical component of 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 15.75 meters.
To calculate the vertical displacement of the Martian rover, we'll use the following formula:
Vertical displacement = velocity * time * sine(theta),
where:
- Vertical displacement is the change in the vertical position.
- Velocity is the magnitude of the rover's constant velocity.
- Time is the duration for which the rover has been moving.
- Theta (θ) is the angle between the hill's slope and the horizontal.
Given:
- Velocity = 1.50 meters/second
- Time = 21.0 seconds
- Theta = 30.0°
Now, let's substitute these values into the formula:
Vertical displacement = 1.50 m/s * 21.0 s * sine(30.0°)
To calculate sine(30.0°), we can use either a scientific calculator or a trigonometric table. Sine(30.0°) ≈ 0.5.
Vertical displacement ≈ 1.50 m/s * 21.0 s * 0.5
Solving this equation, we find:
Vertical displacement ≈ 15.75 meters
Therefore, the vertical displacement of the Martian rover after 21.0 seconds is approximately 15.75 meters.