Now let's say, to make matters worse, you need to brake on a downhill section of road, which makes and angle with the horizontal. i. (5 points) Draw a free-body diagram for your car. ii. (5 points) Find the force in the direction of your displacement. Your final answer should not contain the normal force. iii. (5 points) Use the work energy theorem to find the distance the vehicle will travel once you hit the brakes. iv. (5 points) Let's say your headed north on US 89, 10 miles north of Flagstaff, where the grade is 6% for about 4 miles. It's January and the road is icy. Find the distance required to stop if your initial speed is 65 mph. Find it both without and with including a 1.5 second reaction time. [Grade is the drop in height as a percent of the horizontal distance travelled.]