SOLUTION: a car is driven east for a distance of 34km, then north for 18km,then in a direction 30 degrees east of north for 25km. Determine the magnitude of the displacement(in kilometers) o

Algebra ->  Volume -> SOLUTION: a car is driven east for a distance of 34km, then north for 18km,then in a direction 30 degrees east of north for 25km. Determine the magnitude of the displacement(in kilometers) o      Log On


   

Question 320589: a car is driven east for a distance of 34km, then north for 18km,then in a direction 30 degrees east of north for 25km. Determine the magnitude of the displacement(in kilometers) of the car from its starting point.
Answer by mananth(16946) About Me  (Show Source):
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a car is driven east for a distance of 34km, then north for 18km,then in a direction 30 degrees east of north for 25km. Determine the magnitude of the displacement(in kilometers) of the car from its starting point.
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Draw a sketch to understand the problem.
start from A
A to B east = 34 km
B to C north = 18 km
C to D 30 deg north of east 25km
the horizontal distance traveled from C will be 25* cos 30 = 21.6 km
Total distance traveled eastwards = 34+21.6 = 55.6 km
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Distance traveled north from B to C = 18 km
distance traveled vertical will 25*sin30=12.5 km
Vertical distance traveled = 12.5 + 18.5=31
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The direct distance from start to end is the hypotenuse of a right triangle whose legs are 55.6 km & 31 km
55.6 ^2 + 31^2 =4052.36
sqrt 4052.36 is the direct distance from start to the end
= 63.65 km