A car travels along a straight road, heading West for 3 hours, and then travels NE on another road for 2 hours. If the car has maintained a constant speed of 55 mi/hr, how far is it from its starting point?© BrainMass Inc. brainmass.com September 28, 2022, 2:40 am ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
If we take the East as positive x direction and North as the positive direction
When the car travels West it is moving in the negative direction.
Distance traveled in the West direction (negative x direction) = 55 x 3 = 165 miles
When the car travels NE its direction makes an angle of 45 degrees with the positive x direction.
Distance traveled in the NE direction = 55 x 2 = 110 miles
Component of this distance in the x direction= 110 Cos 45 = 77.78 miles
Component of this distance in the y direction= 110 Cos 45 = 77.78 miles
Now we add up the magnitudes of components in the x and y direction
x direction= -87.22 miles =-165+77.78
y direction= 77.78 miles =0+77.78
Resultant r has a magnitude equal to
r^2= x^2+y^2 (^2 means squard)
or r^2= 13657.06 =(-87.22)^2+(77.78)^2
or r= 116.86 =√13657.06
Therefore the car is 116.86 miles from the starting point© BrainMass Inc. brainmass.com September 28, 2022, 2:40 am ad1c9bdddf>