2) A cruise ship is traveling south going approximately 22mph when it hits the Gulf Stream flowing east at 4 mph.
Show your work.
A) What is the vector component for the cruise ship?
B) What is the vector component for the Gulf stream?
C) What is the resultant vector?
D) Find the resultant velocity. Round to the nearest tenth.
E) Find the resultant direction. Round to the nearest tenth.
A) The vector component for the cruise ship is 22 mph south.
B) The vector component for the Gulf stream is 4 mph east.
C) To find the resultant vector, we need to use the Pythagorean theorem:
resultant vector = √(22^2 + 4^2) = √500 ≈ 22.4 mph
D) To find the resultant velocity, we divide the resultant vector by the time interval, assuming it is constant. We don't have a time interval given, so we can't calculate this.
E) To find the resultant direction, we use trigonometry:
resultant direction = arctan(4/22) ≈ 10.5° east of south
To solve this problem, we need to break down the velocities into their respective vector components and then find the resultant vector.
A) The vector component for the cruise ship traveling south at 22 mph can be represented as (0, -22) mph. The y-component is negative because it is traveling south (opposite to the positive y-axis direction).
B) The vector component for the Gulf Stream flowing east at 4 mph can be represented as (4, 0) mph. The x-component is positive because it is flowing east (in the positive x-axis direction).
C) To find the resultant vector, we add the individual vector components together:
Resultant vector = (0 + 4, -22 + 0) mph
Resultant vector = (4, -22) mph
D) To find the resultant velocity, we calculate the magnitude of the resultant vector:
Resultant velocity = √(4^2 + (-22)^2) mph
Resultant velocity = √(16 + 484) mph
Resultant velocity = √500 mph
Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)
E) To find the resultant direction, we calculate the angle formed between the resultant vector and the positive x-axis using the arctan function:
Resultant direction = arctan((-22)/4) degrees
Resultant direction ≈ -79.3 degrees (rounded to the nearest tenth)
To solve this problem, we need to break down the velocities into vector components and then find the resultant vector, velocity, and direction.
A) To find the vector component for the cruise ship, we need to consider its velocity in the south direction. Since the ship is traveling south at 22 mph, the vector component in the south direction would be (-22, 0) mph.
B) To find the vector component for the Gulf Stream, we need to consider its velocity in the east direction. Since the Gulf Stream is flowing east at 4 mph, the vector component in the east direction would be (0, 4) mph.
C) To find the resultant vector, we need to add the vector components of the cruise ship and the Gulf Stream.
Resultant vector = (-22, 0) + (0, 4)
= (-22, 4) mph
D) To find the resultant velocity, we need to calculate the magnitude of the resultant vector using the Pythagorean theorem.
Resultant velocity = √((-22)^2 + 4^2)
= √(484 + 16)
= √500
≈ 22.4 mph (rounded to the nearest tenth)
E) To find the resultant direction, we need to calculate the angle that the resultant vector makes with the south direction. We can use the inverse tangent function:
Resultant direction = arctan((4/22))
≈ 10.1 degrees (rounded to the nearest tenth)
Please note that the resultant direction is the angle with respect to the south direction, not the east or west directions.