If an airplane is flying directly north at 300.0 km/h, and a crosswind is hitting the airplane at 50.0 km/h from the east, what is the airplane's resultant velocity?

magnitude = 304.14 km/h

direction: West of North

Explanation:

The final plane's vector velocity will be the result of the vector addition of one pointing North of length 300 km/h, another one pointing West of length 50 km/h.

To find the magnitude of the final velocity vector (speed) we need to apply the Pythagorean theorem in a right angle triangle with sides: 300 and 50, and find its hypotenuse:

km/h

The actual direction of the plane is calculated using trigonometry, in particular with the arctan function, since the tangent of the angle can be written as:

So the resultant velocity vector of the plane has magnitude = 304.14 km/h,

and it points West of the North direction.

200 revolutions per minute = 20.9 rad/s

Explanation:

It is given that, a figure skater is rotating at a rate of 200 revolutions per minute. It is the angular velocity of the skater. We have to convert it into radian/second.

Revolution per minute can be converted to radian per minute as :

Since, 1 radian/second = 60/2π revolutions per minute

So, 1 revolution/minute = 2π/60 radian/second

200 revolution/minute = 200 × 2π/60 radian/second

200 revolution/minute = 20.9 radian/second

Hence, this is the required solution.