A virus is sneezed out at a rate of 45 m/s. It travels through the air and makes contact with a stationary person nearby. The stationary person appears unaffected. Which of the following statements is always true?

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Correct Answer: **B.** *In the case of an inelastic collision, the person’s momentum is changed by a factor of a little bit less than 45.*

We will need to analyses each statement to check to see if it is always true.

A.) By Newton’s 3rd law we can see that the person does indeed apply a force upon the virus, even though she is stationary. The force will be equal but opposite to that of the virus’s force. By Newton’s 2nd law the force the virus applies is proportional to its mass, not the person’s mass. This answer choice is incorrect.

B.) Momentum is mass times velocity, and must be conserved in any collision situation. In the case of an inelastic collision, the masses stick together at the end.

The initial conditions must equal the final conditions for momentum to be conserved. The combined velocity is negligibly small and can be set to zero as the person was not apparently affected.

The person’s momentum is affected by a factor of 45.

C.) An elastic collision will have the same initial conditions as the inelastic collision. The difference is in the final conditions; the masses will not stick together.

Conserving the momentum, the person will have a end velocity indirectly proportional to her mass. This answer choice is incorrect.

D.) We can assume there is no apparent potential energy in the system. The only energy that exists is kinetic. In the initial condition the kinetic energy is only shown in the virus. This is enough to show that the statement is incorrect as the person has no energy.

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Photo attributed to ScientificRelevance.