# Relative motion

#### werehk

PHF Hall of Fame
A helicopter is trying to land on a ship deck which is drifting south (unit vector $$\displaystyle y_0$$ )at 17m/s. A 12m/s wind is blowing from east (unit vector $$\displaystyle x_0$$ ). The ship crew sees the helicopter descending at 5 m/s. Take the downwards direction as unit vector $$\displaystyle z_0$$ . What is its velocity relative to water and air?

This is a multiple choice question, but the I'm too lazy to type all of them

$$\displaystyle -12x_0 + 17y_0 + 5z_0$$ and $$\displaystyle 17y_0 + 5z_0$$?

#### topsquark

Forum Staff
A helicopter is trying to land on a ship deck which is drifting south (unit vector $$\displaystyle y_0$$ )at 17m/s. A 12m/s wind is blowing from east (unit vector $$\displaystyle x_0$$ ). The ship crew sees the helicopter descending at 5 m/s. Take the downwards direction as unit vector $$\displaystyle z_0$$ . What is its velocity relative to water and air?

This is a multiple choice question, but the I'm too lazy to type all of them

$$\displaystyle -12x_0 + 17y_0 + 5z_0$$ and $$\displaystyle 17y_0 + 5z_0$$?
You seem to have the answers backward. The question is asking "relative to water and air" and your answers are "relative to air and water."

-Dan

werehk

#### werehk

PHF Hall of Fame
Could you teach me how to deal with problem on relative motion,please?
Are there steps in solving these problems?

Would the wind blowing affect the moving helicopter?

(I reply late as my Internet has got a problem)

#### topsquark

Forum Staff
Typically there are three ingredients to a relative motion problem. Something is stationary (ground usually), the velocity of a medium (water or air) given with respect to the stationary object and the velocity of an object which is in the medium.

It is useful to know that
$$\displaystyle \vec{v_m} = \vec{v_o} + \vec{v}$$
where $$\displaystyle v_m$$ is the net velocity of the object in the medium measured with respect to the stationary object, $$\displaystyle v_0$$ is the velocity of the object measured with respect to the stationary object when the medium is not moving, and v is the velocity of the medium measured with respect to the ground.

A standard problem is a boat that has a speed of 20 m/s in still water, crossing a river (the current flowing at 4 m/s). If the boat is to move straight across the river what angle does the boat have to be pointing in and what is the net speed of the boat with respect to the ground?

I'll let you work that if you like, and you can show me what you have been able to do with it.

-Dan

#### werehk

PHF Hall of Fame
Let $$\displaystyle \theta$$
Constructing a triangle with magnitude of hypotenuse equals to 20 and with opposite side magnitude equals 4

Therefore $$\displaystyle \theta$$ equals 11.53 degree approximately

For the net speed, by pythagoras' theorem , net speed is approximately 19.6m/s

Am I right?

#### topsquark

Forum Staff
Let $$\displaystyle \theta$$
Constructing a triangle with magnitude of hypotenuse equals to 20 and with opposite side magnitude equals 4

Therefore $$\displaystyle \theta$$ equals 11.53 degree approximately

For the net speed, by pythagoras' theorem , net speed is approximately 19.6m/s

Am I right?
You have done well, grasshopper.

-Dan

werehk