Answer:
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.
The average speed is determined by the following formula:
average speed = [sum of (speed * time for which that speed was traveled)] / total time
average speed = [(83 * 26 + 41 * 52 + 60 * 45 + 0 * 15) / 60] / [(26 + 52 + 45 + 15) / 60]
*note: The division by 60 is to convert minutes to hours. We see that the 60 cancels from the top and bottom of the division
average speed = 50.65 km/hr
The total distance traveled is equivalent to the numerator of the fraction we used in the first part. This is:
Distance = (83 * 26 + 41 * 52 + 60 * 45 + 0 * 15) / 60
Distance = 116.5 kilometers
(30, 5)
(10, 1)
change of y / change of x
= (30 - 10) / (5 - 1)
= 20 /4
= 5
Answer
Around 400 B.C.E, the Greek philosopher Democritus introduced the idea of the atom as the basic building block matter. Democritus though that atoms are tiny, uncuttable, solid particles that are surrounded by empty space and constantly moving at random.
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