Ships A and B leave port together. For the next two hours, ship Atravels at 20 mph in a direction 30° west of north while theship B travels 20° east of north at 25 mph.
a. What is the distance between the two ships two hours after theydepart?
b. What is the speed of ship A as seen by ship B?

The answers to the question are

a. The distance between the two ships two hours after they depart is 39.1 miles

b. The speed of ship A as seen by ship B is 12.14 m/h south and 15.32 m/h east or Ship B sees ship A has having a magnitude velocity of 19.5 m/h ∡38.4 ° South East

Explanation:

Firstly we list out the known variables as follows

Ship A velocity = 20 m/h  

Ship A direction = 30 ° West of North

Ship B velocity = 25 m/h

Ship B direction = 20 ° East of North

Distance covered after 2 hours for ship A = 20×2 = 40 miles

Distance covered after 2 hours for ship B = 25×2 = 50 miles

Dx component of ship A = 40×sin (30) = -20 miles and Dy = 40×cos (30) = 34.64 miles

While for ship B, we have

Dx = 50×sin (20) = 17.1 miles and Dy = 50×cos (20) = 46.98 miles

Therefore, the distance between the two ships is

((Ship B Dx - Ship A Dx)^2 +Ship B Dy - Ship A Dy)^2)^0.5

=((17.1-(-20))^2 + (46.98-34.64)^2)^0.5 = 39.1 miles

The speed of ship A as seen by ship B can be found by

The vy of ship A relative B = 20 cos 50 =  12.86 m/h

Therefore relative to ship B ship A is moving at a speed of 12.86 m/h - 25 m/h   = -12.14 m/h north and 20 sin 50 or 15.32 m/h east

or 12.14 m/h south and 15.32 m/h east having a magnitude of  19.5 m/h 38.4 ° South East

This is solved graphically by the attached diagram, the required vector is the line between the green and blue dots

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.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y