SOLUTION: Two ships leave Liverpool at the same time. One of them travels north-west at an average speed of 10.5 km/h while the other travels at an average speed of 14 km/h on a bearing of
Algebra.Com
Question 1110434: Two ships leave Liverpool at the same time. One of them travels north-west at an average speed of 10.5 km/h while the other travels at an average speed of 14 km/h on a bearing of 280ᐤ. How far apart are these ships after 2 hours?
I do not understand this because, unless I'm mistaken, a bearing angle of 280ᐤ is going north-west, and the question doesn't say what angle the first ship is going on. I also do not know how to figure out how far apart they are after two hours. Help would be much appreciated!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two ships leave Liverpool at the same time. One of them travels north-west at an average speed of 10.5 km/h while the other travels at an average speed of 14 km/h on a bearing of 280ᐤ. How far apart are these ships after 2 hours?
:
Exactly northwest is 315 degrees so the angle between the two ship's path is:
315-280 = 35 degrees
Find the distance each ship has traveled in two hrs; dist = time * speed
2*10.5 = 21 km
and
2*14 = 28 km
We have a triangle we can solve; the enclosed angle is 35 degrees (A), has legs of 21 and 28 km. the distance between the ships is the side opposite this angle a
Use the law of cosines a^2 = b^2 + c^2 - 2(b*c)cos(A)
In this problem
a^2 = 21^2 + 28^2 - 2(21*28)Cos(35)
a^2 = 441 + 784 - 2(588)*.819
do the math
a =
a = 16.17 km apart after two hours
:
this is the method, I'll let you check my math.
RELATED QUESTIONS
Two ships depart a port at the same time. One travels 11 degrees west of south at 45 mph... (answered by stanbon)
Two speedboats head off from the same point on a lake at the same time. One heads north... (answered by josgarithmetic)
Two ships leave port at the same time. Ship A sails north at a speed of 10 mph while ship (answered by ankor@dixie-net.com)
Two ships leave port at the same time. One ship takes a bearing of 26± East of due... (answered by lwsshak3)
Two boats leave a port at the same time. One boat sails 2.2 km/h at 33o east of north.... (answered by ikleyn)
Two drivers leave home at the same time and travel on straight roads that diverge by 70... (answered by ankor@dixie-net.com)
A container ship left Hawaii and traveled north at an average speed of 5 km/h. A cruise... (answered by greenestamps)
Two airplanes leave Toronto at the same time, one travelling west and the other east.... (answered by nerdybill)
Two trains leave the railway station at the same time.The first travels due west and... (answered by ankor@dixie-net.com)