A ship leaves port at 1:00 P.M. and sails in the direction N36°W at a rate of 25 mi/hr. Another ship leaves port at 1:30 P.M. and sails in the direction N54°E at a rate of 16 mi/hr.
(a) Approximately how far apart are the ships at 3:00 P.M.? (Round your answer to the nearest whole number.)
(b) What is the bearing, to the nearest degree, from the first ship to the second?
Did you make a diagram?
Did you realize that the angle between their paths is 90°
How easy is that ???
First ship goes for 2 hrs at 25 mph or distance = 50 miles
2nd ship goes for 1.5 hrs at 16 mph or distance = 24 miles
a) let x be the distance between them
x^2 = 50^2 + 24^2 = 3076
x = 55.46 km
Let the angle at the left of the triangle be Ø
tanØ = 24/50
Ø = appr 25.64°
Draw in horizontals and verticals at that vertex and you should be able to find the bearing between the two ships
ok, sorry, would you help me then, please
ok, thanks
Help me for that question
To solve this problem, we can use the concept of velocity vectors to determine the positions of the ships at 3:00 P.M.
(a) To find the position of the first ship at 3:00 P.M., we need to determine the time elapsed since it left port at 1:00 P.M. The time interval from 1:00 P.M. to 3:00 P.M. is 2 hours.
The first ship sails in the direction N36°W at a rate of 25 mi/hr. To determine how far it has traveled in 2 hours, we can multiply its speed by the time: distance = speed * time = 25 mi/hr * 2 hr = 50 miles.
Therefore, the first ship is approximately 50 miles away from the port at 3:00 P.M.
(b) To find the position of the second ship at 3:00 P.M., we need to determine the time elapsed since it left port at 1:30 P.M. The time interval from 1:30 P.M. to 3:00 P.M. is 1.5 hours.
The second ship sails in the direction N54°E at a rate of 16 mi/hr. To determine how far it has traveled in 1.5 hours, we can multiply its speed by the time: distance = speed * time = 16 mi/hr * 1.5 hr = 24 miles.
Therefore, the second ship is approximately 24 miles away from the port at 3:00 P.M.
To find the distance between the two ships at 3:00 P.M., we can use the Pythagorean theorem since they form a right triangle. The distance between the ships is the hypotenuse of this triangle.
Using the distance formula, we can calculate the distance between the two ships:
distance = √((50^2) + (24^2))
distance = √(2500 + 576)
distance = √(3076)
distance ≈ 55.5 miles
Therefore, the ships are approximately 56 miles apart at 3:00 P.M.
To find the bearing from the first ship to the second, we can use the concept of angle of inclination. The angle of inclination can be calculated using the inverse tangent function.
tan(θ) = opposite/adjacent
tan(θ) = 24/50
θ ≈ tan^(-1)(24/50)
θ ≈ 26.5°
However, this angle is measured from the north direction. Since the second ship is to the east of the first ship, subtracting this angle from 90° will provide us with the bearing from the first ship to the second.
Bearing = 90° - 26.5°
Bearing ≈ 63.5°
Therefore, the bearing from the first ship to the second ship is approximately 64°.