Question

A plane flies 459 km east from city A to city B in 41.0 min and then 909 km south from city B to city C in 1.80 h. For the total trip, what are the (a) magnitude (in km) and (b) direction of the plane's displacement, the (c) magnitude (in km/h) and (d) direction of its average velocity, and (e) its average speed (in km/h)? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east). for

a) Magnitude = sqrt(459^2+(-909)^2) = 1018 km
b) Angle = inverse tangent (-909/459) = -63.2(degrees)
c) sqrt((459/(41/60))^2 + (-909/1.80)^2)= 840.3
d) Angle = inverse tangent (-505/672)= -36.9

Answer 1

This high school physics question deals with calculating a plane's displacement, average velocity, and speed after flying in two segments, combining concepts of kinematics and vector analysis using trigonometry and the Pythagorean theorem.

Step-by-step explanation:

The question relates to the topic of kinematics in physics, specifically questions involving displacement, velocity, and vectors. These questions require understanding how to calculate the resultant of multiple displacement vectors, determine the magnitude and direction of the resulting displacement, and calculate average speeds and velocities from given distances and times.

A critical concept in these types of problems is the use of trigonometry to resolve vectors into their components. For example, when a plane flies 459 km east and then 909 km south, the total displacement can be found using the Pythagorean theorem. The direction of the displacement is given by the inverse tangent (arctan) of the ratio of the southern to eastern components. Similarly, the average velocity can be determined using the total displacement divided by the total time, considering its direction as well.

Calculating average speed involves dividing the total distance traveled by the total time taken, where the direction does not affect the result as it is a scalar quantity.