Chapter 04, Problem 008 A plane flies 403 km east from city A to city B in 41.0

Question

Chapter 04, Problem 008 A plane flies 403 km east from city A to city B in 41.0 min and then 868 km south from city B to city C in 1.10 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east) (a) Number (b) Number (c) Number (d) Number (e) Number Units km Units o (degrees) Units km/h Units o (degrees) Units km/h

Explanation / Answer

given

from A to B , s1 = 403 km displacement and from B to C s2 = 868 km  

and time period s are t1 = 41 min = 41/60 hr = 0.683 hr , t1= 1.10 hr

writing the displacement vectors

s1 = 403 km i + 0 km j

s2 = 0 km i - 868 km j

the magnitude of the displacement is s2-s1

s = (0 km i - 868 km j ) - (403 km i + 0 km j )

s = (-403 km i -868 km j )

the magnitude is  

s = sqrt( (-403)^2+(-868)^2) km = 956.99 km = 957 km

the direction is  

tan theta = (-868/-403)

theta = 65.09 degrees

average velocity is v avg = s2-s1/(t2-t1) = (-403 km i -868 km j ) /(1.10+0.683) km/hr = -712.84352 km /hr

v1 = 590 km /hr i + 0 km/hr j ,

v2 = 0 km/hr i - 789.09 km /hr j

the speed is V = sqrt(590^2+789.09^2) m/s = 985.27 m/s

the direction is theta = arc tan ( 789.09/590) = 53.21 degrees

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