0192837465 said:

Please help with the following question:

Suppose a policeman traveling at 5 m/s is firing his gun at a rate of 20 bullets per minute is chasing a bank robber who is peddling his Huffy at 50 m/s. At what rate do the bullets reach the bank robber (use 500 m/s for the speed of a bullet)?

ANSWER IS: 18 bullets/min

The method I used was by the equation: f' = f[(V+/-Vd)/(V-/+Vs)]

f' = detected frequncy

f = source frequency

v = rate of fire (frequency) of bullet fire

vd = velocity of detector

vs = velocity of source

When choosing +/- for the numerator, consider the relative velocity of the detector. The robber (detector) moves away the police officer (source) that decreases the detected frequency. To decrease the frequency in the numerator, a minus sign must be used.

The same logic is used in the denominator. What is the velocity of the source doing to the frequency? The policeman (source) moves toward the robber (detector) that should increase frequency. To increase the detected frequency (f'), a minus sign is used to decrease the denominator.

With this said, you get the equation: f' = f[(V -Vd)/(V- Vs)]

Plug in the variables: f' = (20)[(500-50)/(500-5)] = (20)(450/495)

For the MCAT, an equation to work out like this will take a long time, so I round the denominator. It changes the answer somewhat, but you can eliminate choices based on this final approximation.

f' = (20)(450/495) = (20)(450/500) = (20)(900/1000) = (20)(0.9) = 18 bullets per minute

In the MCAT, you may see answers such as:

A. 17.8 bullets per minute

B. 18 bullets per minute

C.18.2 bullets per minute

D. 22 bullets per minute

In this case, since we increased the denominator, the answer should be slightly greater than the approximation. Hence, A can be canceled. 18 bullets per minute is merely an approximation, so it can be canceled. From our work, the bullet rate should decrease and in D., the bullet rate increases. It can be canceled. The answer is C.

In the MCAT, they expect you to approximate to simplify the work, I'm sure the answer choices won't be as complicated as this. I hope this explains your question thoroughly. I'd gladly clarify anything I missed.