(Solved): Please Help solve Part B (11\%) Problem 4: A car moves along a horizontal road with constant veloci ...

Please Help solve Part B

(11\%) Problem 4: A car moves along a horizontal road with constant velocity \[ \vec{v}_{0}=v_{0, x} \hat{i} \] until it encounters a smooth inclined hill. It climbs the hill with constant velocity \[ \vec{v}_{1}=v_{1, x} \hat{i}+v_{1, y} \hat{j} \] as indicated in the figure. A Cartesian coordinate system has been indicated. \( 50 \% \) Part (a) If the car moves for equal times along the road and hill, create an expression for its average velocity vector, \( \vec{v}_{\text {ave }} \), in terms of \( v_{0, x}, v_{1, x} \), and \( v_{1, y} \) along with the unit vectors \( \hat{i} \) and \( \hat{j} \). \( \vec{v}_{\mathrm{ave}}=\left(\mathrm{v}_{0 \mathrm{x}} \mathbf{i}+\mathrm{v}_{1 \mathrm{x}} \mathbf{i}+\mathrm{v}_{1 \mathrm{y}} \mathbf{j}\right) / 2 \quad \checkmark \) Correct! \( \nabla 5 \) 50\% Part (b) Create an expression for the direction of the car's average acceleration in terms of \( v_{0, x}, v_{1, x} \), and \( v_{1, y} \) during the transition between the horizontal surface and the hill. Express the answer in terms of \( \tan (\theta) \), where \( \theta \) is the angle of the average acceleration vector relative to the horizontal.