Exercise Ch.4#14: A Self-Driving Car Trust the method-Goooood sketches and variables. You have everything you need! 1. A car drives itself from Reno, Nevada to Utah. That is one incredibly straight stretch of highway! Let's model it as perfectly straight. The speed limit is 80 mi/h ("mph"), so cruise control is set at that even though some of us would prefer 100 mi/h. a. If the car stays on a straight path at 80.0 mi/h, what is its acceleration? b. Show the work to convert 80.0 mi/h to km/h. Then show the conversion to m/h. Finally, show the conversion to m/s. c. Write down ("show") what the constant acceleration equations look like when the acceleration is a constant 0 ... In words, what do the equations "say"? Write them, without putting in numbers, with subscripts for state 1 to 2 and then write them again using subscripts for states 2 and 3. d. [Read this quickly and then reread slowly. As you read it a second time, sketch the process, show key states, well-labeled variables, and your coordinate choice. You might also want to make a table of your data: Given (G), Implied (1), and Wanted (W).] The total distance along the road is about 395 mi. We are pretending ("modeling") the road is perfectly straight. The first stretch, to Winnemucca, NV, is 173 mi and the car maintains 80.0 mi/h. Oh Nooooo! Road work! The car travels the last stretch of road at a constant velocity in 4 h and 56 min. How fast was the car going on the last section? e. Before putting in numbers, write an equation with helpful subscripts to show the total time of the trip from state 1 to state 3. Find what you need to calculate the total trip time. 2. What if the car in the last puzzle wasn't working quite right and increased speed over the first leg (Reno to Winnemucca) at a rate of 0.010 mi/h every second? Sketch it! a. [HUGE: Convert the acceleration to mi/h and work with those units. Also, write all three constant acceleration equations for state 1 to 2 without numbers yet. Put checkmarks over the variables you have values for. Circle what you want. Choose the easiest algebraic path!] It still started at 80.0 mi/h, but now at what speed would it be traveling when it passed Winnemucca? Comment on your result. b. How long would this take in hours and minutes? (Go back to those eq'n you wrote.) c. If there was no road work, and the car had to slow to 65 mi/h by the time it crossed into Utah, what acceleration would it have to set for itself to do this with a constant rate of slowing? (Now write all three eq'ns using states 2 and 3!! Solve the puzzle.) d. For this crazy ride, how long would the total trip be? (Always write general expressions with subscripts before putting in numbers! This is such a powerful habit!)Exercise Ch.4#15: You Take the Lead! I'm going to ask questions and not lead you through the steps. Lay out everything you know-the puzzle pieces! To drive in a spy movie, Carson must do the following perfectly. Start from rest and increase speed with an acceleration of 8.0 m/s for 3.0 s. He must then coast (keep same speed) for 1.0 s, and then apply the brakes to stop with a constant acceleration in 20.0 m. Once stopped, he must take virtually no time and put it in reverse to accelerate backward until he is 30.0 m in front of where he started the scene and traveling backward at 16.0 m/s. [OK, one hint. Get the At and Ax between each two states. You have everything you need. Explore by moving the puzzle pieces around on paper. Be careful with the +/- signs!] FOOD STOUD a. How much time did this all take? b. What is Carson's displacement when backing up?Exercise Ch.4#16: My Love! Sketch is key! When you have two objects, imagine taking pictures (or hitting pause). Draw both objects at each of the instants (states) needed. You are out jogging around Lake Merritt. You ("Y") happen to glance behind you and notice your high school crush ("H") is half a football field behind you (say 50.0 m) ... good eyes! Now H is jogging at the same speed as you, which you know from your smart watch to be 4.5 m/s. a. At what rate would you have to casually decrease speed in order for H to catch up to you in 45.0 s? Assume your acceleration is constant and sketch both of you at the two snapshot times! HINT: On your picture, show how Ax, is related to Axy. Where is the 50.0 m on your sketch? Write the equations for each, with subscripts, and THEN see where to go! b. If you maintained that acceleration, what speed would you be traveling when H passes you? ("Oh, hi! What a coincidence!")Exercise Ch.4#17: Ski Patrol! 21571 Don't look at the solution. Get all the pieces on paper and fight for it. Positive struggle is the mark of all winners. Kristin gets off the chair lift, puts on her poles, and starts skiing down the slope accelerating at 3.5 m/s2. Meanwhile, Julia is just learning to snowboard, traveling at a constant 6.2 m/s, and is heading straight across Kristin's path! Julia is 8.4 m from where their paths would cross and Kristin is 5.2 m from that place. a. Prove whether or not they hit. b. At what speed would Julia have to be traveling for them to hit?Exercise Ch.4#18: Newton and Steph Curry! Sketch is key! When you have two objects, imagine taking pictures (or hitting pause) at each of the instants (states) needed. Write equations for each object separately and figure out the connections. For example, the velocity of the apple at state 1 could be up, and that of the ball could be vp . The displacements would be Ay A,142 and AyB, 142' Sir Isaac Newton throws an apple downward from a window. The apple is 25.0 m above the ground when Newton releases the apple at a speed of 18.0 m/s. The great basketball player Steph Curry is below. He throws a basketball upward and releases it at the same time Newton releases his apple. The basketball starts at 12.0 m/s upward and 2.3 m above the ground. The apple and basketball hit ... when and where?! [HINT: Start by drawing the ground and then the instant both are released. Show/label everything you know. Then show the second instant of interest. Construct the equations and explore! Be sure to write down what is implied in the description of the process.] from a. Choose vertically up to be the + direction for both and find out when and where they hit. Care MUST be taken with the + signs of velocity, displacement, and acceleration-see them on the sketch! Then construct the constant acceleration equations for both objects and work the algebra. First, show on you picture why it is implied that: niggsnib owt arif to rod Ayaz - AyAlzz = 22.7 m b. Now choose vertically down to be the + direction for both. What changes? Without doing the problem over entirely, modify the work and results you got in part a to reflect this