A sailor climbs a mast at 0.5 m/s on a ship travelling north at 12 m/s, while the current flows east at 3 m/s. What is the speed of the sailor relative to the ocean floor?
assuming the usual orientations, the resultant is
v = 3i + 12j + 0.5k
so the speed is |v| = √(3^2 + 12^2 + 0.5^2) = 12.38 m/s
horizontal speed = sqrt (3*2 + 12*2)
vertical speed= 0.5
so speed = sqrt ( 3^2+ 12^2 + 0.5^2)
luckily the question did not ask for velocity :)
Well, if the sailor climbs any higher on that mast, they might just touch the clouds! But let's focus on the question at hand.
To find the speed of the sailor relative to the ocean floor, we need to add up all the velocities involved.
The sailor is climbing at a speed of 0.5 m/s, and the ship is moving north at 12 m/s. Since these are in different directions, we subtract the sailor's speed from the ship's speed to get the relative velocity of the sailor with respect to the ship, which is 11.5 m/s north.
Now, we need to take into account the current flowing east at 3 m/s. Since this velocity is perpendicular to the northward velocity of the ship, we can use the Pythagorean theorem to find the resultant velocity.
We square the velocities, add them up, and take the square root of the result.
So, the speed of the sailor relative to the ocean floor is like solving a fun math puzzle! It's the square root of (11.5² + 3²) m/s. I'll leave it to you to grab your calculator and solve it. Just remember, don't get lost in the waves of numbers!
To find the speed of the sailor relative to the ocean floor, we need to consider the velocities of the sailor, ship, and current separately.
Given:
Speed of the sailor climbing the mast (upward velocity) = 0.5 m/s
Speed of the ship traveling north = 12 m/s
Speed of the current flowing east = 3 m/s
To find the speed of the sailor relative to the ocean floor, we need to combine both the vertical and horizontal components of the velocities.
Vertical Component:
The speed of the sailor climbing the mast (0.5 m/s) is directed upward, and it remains the same relative to the ocean floor. Therefore, the vertical component of the sailor's velocity relative to the ocean floor is still 0.5 m/s.
Horizontal Component:
The speed of the ship traveling north at 12 m/s and the current flowing east at 3 m/s are perpendicular to each other. Thus, we can use the Pythagorean theorem to find the resultant speed.
Using the Pythagorean theorem:
Resultant Speed = √(Ship Speed^2 + Current Speed^2)
= √(12^2 + 3^2)
= √(144 + 9)
= √153
≈ 12.37 m/s
Therefore, the speed of the sailor relative to the ocean floor is approximately 12.37 m/s (resultant speed).
To find the speed of the sailor relative to the ocean floor, we need to separate the sailor's motion into two components: one parallel to the ocean floor and one perpendicular to it.
Let's break down the given information:
- The sailor climbs the mast at 0.5 m/s (vertically upwards).
- The ship is moving north at 12 m/s.
- The current flows east at 3 m/s.
We can treat the ship's velocity and the current's velocity as vectors. The vertical component of the sailor's velocity is simply 0.5 m/s.
To find the horizontal component of the sailor's velocity, we subtract the horizontal components of the ship's velocity and the current's velocity. Since the ship is moving directly north and the current is flowing east, these velocities are perpendicular to each other. Therefore, the horizontal component of the sailor's velocity is the vector sum of the ship's and current's horizontal components.
Let's calculate the horizontal component of the sailor's velocity:
- The ship's horizontal velocity component is 0 m/s (since it is moving directly north).
- The current's horizontal velocity component is 3 m/s (since it flows east).
So, the horizontal component of the sailor's velocity is 0 m/s - 3 m/s = -3 m/s (negative because it is in the opposite direction to the current).
Now, we can use the Pythagorean theorem to find the speed of the sailor relative to the ocean floor:
Speed^2 = (Vertical Component)^2 + (Horizontal Component)^2
Speed^2 = (0.5 m/s)^2 + (-3 m/s)^2
Speed^2 = 0.25 m^2/s^2 + 9 m^2/s^2
Speed^2 = 9.25 m^2/s^2
Taking the square root of both sides, we find:
Speed = √9.25 m^2/s^2
Speed ≈ 3.04 m/s
Therefore, the speed of the sailor relative to the ocean floor is approximately 3.04 m/s.