Help!
Ships A and B leave port at the same time and sail on straight paths making an angle of 60 degrees with each other. HOw far apart are the ships at the end of 1 hour if the speed of ship A is 25 km/h and that of ship B is 15 km/h?
after 1 hours, one ship has gone 25 km, the other 15 km
make a sketch, let the distance between them be x
straigh-forward case of the cosine law
x^2 = 25^2 + 15^2 - 2(25)(15)cos 60°
= ....
you do the arithmetic.
(I got appr 21.8 km)
Thanks a lot.
To determine how far apart the ships are at the end of 1 hour, we can break this problem into two components: the horizontal distance and the vertical distance between the ships.
First, let's calculate the horizontal distance traveled by both ships after 1 hour.
For ship A:
Distance = Speed * Time
Distance = 25 km/h * 1 hour
Distance = 25 km
For ship B:
Distance = Speed * Time
Distance = 15 km/h * 1 hour
Distance = 15 km
Now, let's calculate the vertical distance between the ships after 1 hour using trigonometry.
Since the angle between the ships is 60 degrees, we can use the sine function to find the vertical distance.
Vertical Distance = Horizontal Distance * sin(60°)
Vertical Distance = 25 km * sin(60°)
Vertical Distance = 25 km * √(3/2)
Vertical Distance = 12.5√3 km
Therefore, the ships are approximately 25 km apart horizontally and 12.5√3 km (or approximately 21.65 km) apart vertically. To find the overall distance between the ships, we can use the Pythagorean theorem.
Distance between ships = √(Horizontal Distance^2 + Vertical Distance^2)
Distance = √((25 km)^2 + (12.5√3 km)^2)
Distance = √(625 km^2 + 187.5 km^2)
Distance ≈ √812.5 km^2
Distance ≈ 28.5 km
Therefore, the ships are approximately 28.5 km apart at the end of 1 hour.
To find out how far apart the ships are at the end of 1 hour, we can use trigonometry.
First, let's calculate the distance covered by each ship in 1 hour.
The distance covered by ship A is given by:
Distance A = speed of ship A × time = 25 km/h × 1 hour = 25 km.
Similarly, the distance covered by ship B is given by:
Distance B = speed of ship B × time = 15 km/h × 1 hour = 15 km.
Now, since the ships are traveling at an angle of 60 degrees with each other, we can consider them as the sides of a triangle. The distance between the ships is the length of the side opposite to the 60-degree angle.
To find this distance, we can use the Law of Cosines. The formula is:
c^2 = a^2 + b^2 - 2ab*cos(C),
where c is the distance between the ships, a and b are the distances covered by ships A and B respectively, and C is the angle between the two sides (60 degrees).
Plugging in the values, we get:
c^2 = (25 km)^2 + (15 km)^2 - 2 × 25 km × 15 km × cos(60 degrees).
Now, we can calculate the distance between the ships:
c^2 = 625 km^2 + 225 km^2 - 2 × 25 km × 15 km × 0.5
c^2 = 625 km^2 + 225 km^2 - 375 km^2
c^2 = 475 km^2
Taking the square root of both sides, we get:
c ≈ √475 km
c ≈ 21.79 km
Therefore, the ships are approximately 21.79 km apart at the end of 1 hour.