A space vehicle is coasting at a constant velocity of 21.1 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.380 m/s2 in the +x direction. After 41.0 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find the following quantities
There are no "following quantities"
How lazy can you get?
To find the following quantities after the RCS thruster is turned off, we can use the equations of motion.
Given:
Initial velocity (v0) = 21.1 m/s in the +y direction
Acceleration (a) = 0.380 m/s^2 in the +x direction
Time (t) = 41.0 s
1. Final velocity in the +y direction (vyf):
Since there is no acceleration in the y direction, the velocity in the y direction remains constant throughout. Therefore, the final velocity in the y direction is equal to the initial velocity in the y direction.
vyf = v0 = 21.1 m/s
2. Final velocity in the +x direction (vxf):
To find the final velocity in the x direction, we can use the equation:
vxf = vxi + at
Since the initial velocity in the x direction (vxi) is 0 m/s, and acceleration (a) is 0.380 m/s^2, we can substitute these values into the equation.
vxf = 0 + (0.380 m/s^2)(41.0 s)
vxf = 15.58 m/s in the +x direction
3. Displacement in the +y direction (dy):
Since the velocity in the y direction is constant, the displacement in the y direction (dy) can be calculated using the equation:
dy = vyi * t
where vyi is the initial velocity in the y direction.
dy = v0 * t
dy = 21.1 m/s * 41.0 s
dy = 864.1 m in the +y direction
4. Displacement in the +x direction (dx):
To find the displacement in the x direction, we can use the equation:
dx = vxi * t + (1/2) * a * t^2
Since the initial velocity in the x direction (vxi) is 0 m/s, we can simplify the equation to:
dx = (1/2) * a * t^2
dx = (1/2) * 0.380 m/s^2 * (41.0 s)^2
dx = 313.57 m in the +x direction
Therefore, the quantities after the RCS thruster is turned off are:
1. Final velocity in the +y direction (vyf): 21.1 m/s
2. Final velocity in the +x direction (vxf): 15.58 m/s
3. Displacement in the +y direction (dy): 864.1 m
4. Displacement in the +x direction (dx): 313.57 m
To find the following quantities, we need to use the kinematic equations to analyze the motion of the space vehicle. Here are the steps to find each quantity:
1. Time taken to stop accelerating:
The time taken to stop accelerating is the time for which the RCS thruster was on. It is given as 41.0 s.
2. Final velocity in the x-direction:
The final velocity in the x-direction can be found using the equation:
vf = vi + at, where
vf = final velocity in the x-direction,
vi = initial velocity in the x-direction (which is zero since the thruster was turned on after the vehicle was coasting), and
a = acceleration in the x-direction.
Plugging in the values, we have:
vf = 0 + (0.380 m/s^2) * (41.0 s)
Solving the equation will give us the final velocity in the x-direction.
3. Displacement in the x-direction:
The displacement in the x-direction can be found using the equation:
Δx = v*t + 0.5*a*t^2, where
Δx = displacement in the x-direction,
v = initial velocity in the x-direction,
t = time taken (which is 41.0 s), and
a = acceleration in the x-direction.
Plugging in the values, we have:
Δx = (0) * (41.0 s) + 0.5 * (0.380 m/s^2) * (41.0 s)^2
Solving the equation will give us the displacement in the x-direction.
4. Displacement in the y-direction:
The displacement in the y-direction can be found using the equation:
Δy = v*t, where
Δy = displacement in the y-direction,
v = velocity in the y-direction, and
t = time taken (which is 41.0 s).
Plugging in the values, we have:
Δy = (21.1 m/s) * (41.0 s)
Solving the equation will give us the displacement in the y-direction.
5. Total displacement:
The total displacement can be found using the Pythagorean theorem:
displacement = √(Δx^2 + Δy^2)
Plugging in the calculated values of displacement in the x-direction and displacement in the y-direction, we can find the total displacement.
By following the steps mentioned above, you can find the requested quantities related to the motion of the space vehicle.