Asubmarine can detect an approaching enemy submarine using sonar. if a stationary submerged submarine emits a 100khz tone and receives a tone doppler shifted by 200hz, calculate the speed of the enemy submarine if the speed of sound in salt water is 1,482m/s. note: because the echo is off of a moving object, the moving object amplifies the doppler effect by a factor of 2! therefore, the speed must be cut in half. a. 1.0m/s b. 1.5m/s c.2.2m/s od.3.3m/s e. 4.4m/s

B) 1.5 m/s

Explanation:

The apparent frequency will be enhanced due to Doppler effect

If f be the apparent frequency , F be the real frequency  , V be the velocity of sound and v be the velocity of approaching submarine then f is given by

f = F \frac{V+v}{V-v}\\

\frac{f}{F} =\frac{V+v}{V-v}\\  

\frac{f}{F}-1  =\frac{V+v}{V-v}-1\\

\Delta f = \frac{2vf}{V-v}\\

200=\frac{2\times v\times 100\times 1000}{1482-v}\\  

v=1.48 m/s

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.