One ship, sailing east with a speed of 7.5 m/s, passes a certain point at 8A.Mand a second ship sailing north at the same speed, passed the same point at 9:30 A.M. At What time are they closest together and what is the distance between them then?
To find the time when the two ships are closest together, we need to determine the point of intersection of their paths.
Let's consider the first ship. It is sailing in the east direction with a speed of 7.5 m/s. Hence, its position at any time 't' can be represented as (7.5t, 0), as we are assuming the starting point as the origin.
Now, let's consider the second ship. It is sailing in the north direction with the same speed of 7.5 m/s. It passed the same point at 9:30 A.M., which is 1.5 hours after the first ship. Thus, its position at any time 't' can be represented as (0, 7.5(t - 1.5)).
To find when the two ships are closest together, we need to find the point of intersection of their paths. So, we set the x-coordinates and y-coordinates of both ships equal to each other:
7.5t = 0 --> Equation 1 (First ship x-coordinate)
0 = 7.5(t - 1.5) --> Equation 2 (Second ship y-coordinate)
From Equation 1, we find t = 0.
Substituting t = 0 into Equation 2, we find 0 = 7.5(-1.5) = -11.25.
This means that the two equations do not intersect when t = 0. Hence, the two ships do not pass closest to each other at 8 A.M.
Now, let's find when the two ships are closest together by considering different times.
If both ships are traveling at a constant speed, the distance between them will be minimum when their paths are perpendicular to each other. This happens when the second ship has traveled the same distance (7.5t) as the first ship in the perpendicular direction.
Let's set up an equation to find the time when this condition is met:
7.5t = 7.5(t - 1.5)
Simplifying, we get:
7.5t = 7.5t - 11.25
Rearranging, we have:
0 = -11.25
This equation has no solution.
Hence, there is no time when the two ships are closest together.
Therefore, there is no specific time when the two ships are closest together, and there is no distance between them at that time.