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
1.50*21.0 sin 30.0° = 15.75m
To calculate the vertical displacement of the Martian rover, we can use the trigonometric relationship between the velocity, time, and angle of the slope.
First, let's break down the velocity into its horizontal and vertical components. The vertical component of the velocity is given by v_vertical = v * sin(θ), where v is the magnitude of the velocity (1.50 meters/second) and θ is the angle of the slope (30.0°).
v_vertical = 1.50 * sin(30.0°)
v_vertical ≈ 0.75 meters/second
Next, we can calculate the vertical displacement using the formula: displacement = velocity * time. In this case, since the velocity is constant, the vertical displacement will be given by s_vertical = v_vertical * t, where t is the time (21.0 seconds).
s_vertical = 0.75 * 21.0
s_vertical ≈ 15.75 meters
Therefore, the vertical displacement of the Martian rover after 21.0 seconds is approximately 15.75 meters.