An electric car starts at point A on a mountain road that inclines upward at 10∘ above the horizontal. At t=0, the car’s speed along the road is 12m/s. From t=0 onward, the car’s engine produces a constant acceleration of 3.0m/s2 directed along the road (up the incline). At the same time, a steady crosswind exerts a constant sideways acceleration of 1.5m/s2 directed due east, perpendicular to the road. Treat the road as straight and neglect any frictional losses other than those already included in the stated accelerations.
(a) Using a coordinate system with x horizontal and positive to the east, and y vertical and positive upward, derive expressions for the x and y components of the car’s position as functions of time for t≥0.
(b) Calculate the car’s x and y coordinates after 6.0s have elapsed.
(c) Determine the car’s total vertical gain in altitude and its total horizontal eastward displacement during this 6.0s interval.
(d) Compute the magnitude and compass bearing of the car’s velocity at t=6.0s. Express the bearing as an angle measured clockwise from due north.