Final answer:
The work done on the particle to cause it to move to the right at 47.0 m/s is 16.528 J.
Step-by-step explanation:
To calculate the work done on the particle, we need to use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the particle has a mass of 22.0 g (or 0.022 kg) and initially moves to the left at a velocity of 21.0 m/s. The final velocity is given as 47.0 m/s to the right. We can use the equation:
Work = (1/2) * m * (vf^2 - vi^2)
Plugging in the values:
Work = (1/2) * 0.022 * (47^2 - 21^2) = 16.528 J
Therefore, the work that must be done on the particle to cause it to move to the right at 47.0 m/s is 16.528 J.