Suppose that the center of a hurricane (also known as the eye of the hurricane) is moving in a direction 60.0 ° north of west with a speed of 41.0 km/h. The eye of the hurricane maintains this velocity for 3.00 hours and then the hurricane shifts suddenly due north with a new speed of 25.0 km/h. This new velocity is then maintained for 1.50 hours. Calculate the average velocity of the hurricane over the total 4.50 hours. Express your answer in terms of the magnitude (in km/h) and direction with respect to the positive x-axis (i.e. due east)
Suppose that the center of a hurricane (also known as the eye of the hurricane) is
moving in a direction 60.0 ° north of west with a speed of 41.0 km/h. The eye of the hurricane
maintains this velocity for 3.00 hours and then the hurricane shifts suddenly due north with a new
speed of 25.0 km/h. This new velocity is then maintained for 1.50 hours. Calculate the average
velocity of the hurricane over the total 4.50 hours. Express your answer in terms of the magnitude
(in km/h) and direction with respect to the positive x-axis (i.e. due east)
Average velocity:
It is defined as the ratio of the total displacement of a body to the total time taken. Mathematically,
where is the total displacement and is the total time.
If , then its magnitude is given by the formula,
And the direction of average velocity with the positive x-axis is given as,
where are the unit vectors along the x and y-axis respectively.
Assume the east direction to be along the positive x-axis and the north direction to be along the positive y-axis.
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