Another physic prob!?

Question

A ship leaves port and travel on a steady course of 40deg N of due east at a steady speed of 8km.h.
How far due north and due east of the port is the ship after sailing for 1 hr?

I tried using pythagras theorem but it won't work out!

Answer 1

Divide the velocity of the ship into its two components...one component pointing due North, the other pointing due East. These two perpendicular components are independent of each other but get combined when you were given the overall magnitude of the velocity in the question.

If you imagine a Cartesian plane drawn out on the ocean on which the ship is sailing...then the Y-axis would be parallel to the North-South direction and the X-axis would be parallel to the West-East direction.
Now imagine a line which starts at the graph's origin and extends for a distance of 8 (km/h) and is pointing at an angle of 40 degrees North of East. This line has both a horizontal (Eastward) components to it as well as a vertical (Northward) component.
To separate these components we can use trigonometric functions,
v_x = V * cos (angle)
v_y = V * sin (angle)
where v_x and v_y are the x and y (horizontal and vertical / East and North) components of the velocity, V is the overall magnitude of the velocity, and angle is the angle of the velocity vector above the horizontal.

V = 8 km/h
Angle = 40 degrees,

v_x = 8 km/h * cos (40 degrees) = 6.13 km/h
v_y = 8 hm/h * sin (40 degrees) = 5.14 km/h

Now you have the horizontal and vertical components of the velocity separated out for you. (this is where you would be able to use the Pythagorean theorem, but you don’t need to....but if you square both velocity components and add them together it should give you the square of the overall magnitude of the velocity.)

Now to find the horizontal and vertical distances the ship travels, just multiply the time the ship is sailing with the velocity in that direction.
The two velocity components we have found are independent of each other so the motion in one direction does not affect the motion in the other direction.

Distance_East = v_x * time = 6.13 km/h * 1 h = 6.13 km
Distance_North = v_y * time = 5.14 km/h * 1 h = 5.14 km

Answer 2

You need trig to solve this.

The resulting coordinates are given by (cos(40)* 8, sin(40) * 8)

I'll leave you to work out why.

Answer 3

Scalar quantaties are issues like money, mass, and so on. So yep, they are able to be dimensionless!! 5. a, b, c ought to all be in metres and d in seconds. incredibly can't be bothered doing something. sorry i'm busy lol.