## College Physics (4th Edition)

The velocity of the truck relative to the car is $63.3~km/h$ at an angle of $39.6^{\circ}$ south of west.
We can write the car's velocity relative to the road in component from: $v_{cr} = 110~ \hat{j}~km/h$ We can write the truck's velocity relative to the road in component from: $v_{tr} = (-85~sin~35^{\circ}~\hat{i}+85~cos~35^{\circ}~\hat{j})~km/h$ $v_{tr} = (-48.75~ \hat{i}+69.63~\hat{j})~km/h$ We can find the truck's velocity $v_{tc}$ relative to the car: $v_{tr} = v_{tc}+v_{cr}$ $v_{tc} = v_{tr} - v_{cr}$ $v_{tc} = [-48.75~ \hat{i}+(69.63-110)~\hat{j}]~km/h$ $v_{tc} = (-48.75~ \hat{i}-40.37~\hat{j})~km/h$ We can find the magnitude of the truck's velocity relative to the car: $\sqrt{(-48.75~km/h)^2+(-40.37~km/h)^2} = 63.3~km/h$ We can find the direction of the truck's velocity south of west relative to the car: $tan~\theta = \frac{40.37}{48.75}$ $\theta = tan^{-1}(\frac{40.37}{48.75})$ $\theta = 39.6^{\circ}$ The velocity of the truck relative to the car is $63.3~km/h$ at an angle of $39.6^{\circ}$ south of west.