Answer:
A) (26, 882)
B) ship Tiger: Time = 0.164 hours
Ship Lion: Time = 0.257 hours
C) Ship Tiger: 0.164 × 60 = 9.84 minute
Ship Lion: 0.257× 60 =15.42minutes
D) Distance = 290.86
E) Ship Tiger (0, 961)
Ship Lion (105, 0)
Step-by-step explanation:
From the question, we can form the equation of the straight line from the initial and final position of the two ships. Using the general linear equation Y = mx + c. that is
Ship Tiger
Initial position (0, 961)
Final position (318, 0)
M = (0 - 961)/318
M = - 3.02
961 = -961/318(0) + C
C = 961. Hence the equation of the line for ship Tiger will be
Y = - 961x/318 + 961 ...... (1)
Ship Lion
Initial position (105, 0).
Final position (0, 1174).
M = 1174/ -105 = - 11.18
0 = 1174/-105(105) + C
0 = - 1174 + C
C = 1174
The equation of the line for ship Lion will be
Y = - 1174/105(x) + 1174 ..... (2)
At the point of intersection of the paths of the ships, they will have common Y and X. Hence equation 1 is equal to equation 2
- 961x/318 + 961 = -1174/105(x) + 1174
-961/318(x) + 1174/105(x) = 1174 - 961
8.16x = 213
X = 213/8.16 = 26.1
Substitute x in equation 1
Y = -961/318(26.1) + 961
Y = -78.88 + 961
Y = 882.12
Therefore the point of intersection of the paths of the ships is (26, 882)
B) given that Lion will reach her destination in one hour, Tiger – in two hours.
Ship Tiger
distance = root(318^2 + 961^2)
Distance = 1012.25
Speed = distance/time
Speed = 1012.25/2 = 506.12
Distance at the point of intersection will be
Distance = root(26^2 + (882-961)^2)
Distance = root(676 + 6241)
Distance = 83.12
Speed = distance/time
Time = distance /speed
Time = 83.12/506.12
Time = 0.164 hours
Ship Lion
distance = root(105^2 + 1174^2)
Distance = 1178.69
Speed = distance/time
Speed = 1178.69/1 = 1178.69
Distance at the point of intersection will be
Distance = root((26-105)^2 + (882-1174)^2)
Distance = root(6241 + 85264)
Distance = 302.5
Speed = distance/time
Time = distance /speed
Time = 302.5/1178.69
Time = 0.257 hours
C) the time in minute the distance between Lion and Tiger will be the shortest will be
Ship Tiger: 0.164 × 60 = 9.84 minute
Ship Lion: 0.257× 60 =15.42minutes
D) The shortest distance between Lion and Tiger will be achieved by using pythagorean theorem for the the distances at the point of intersection
Root (302.5^2 - 83.12^2)
Distance = 290.86
E) the positions of both ships at the moment when the distance between them is the shortest will be the initial position of both ships
That is
Ship Tiger
Initial position (0, 961)
Ship Lion
Initial position (105, 0).
