Overview
Electronic sharing of this document or its contents, in whole or part, is prohibited BASIC Axes: in order to show that you understand how to handle signs in physics, for this entire assignment you're required to work in a coordinate system in which up is positive and down is negative. Math: To show your understanding of kinematics, using the quadratic formula is off-limits for this Exam. If it seems like using the quad is the only way forward, try calculating another unknown quantity instead, and see where that leaves you. Or contact me for help! Checks: To help you get to 2/2 as quickly as possible, this assignment suggests multiple ways to check your results. But don't put check calculations in your solution. If you're not able to correct errors found by running checks, please contact me for help! Equations: Remember that you can only use equations from the PHYS 1200 Equation Sheet, and must write them down as they appear there before you start doing algebra or filling in values. Using physics eqns that aren't on the eqn sheet will result in a score of 0/2 until the solution is revised. See Exam Info > Equations. Questions Fastball (FB) is a superhero who can fly, and also throw any object as fast as a jet aircraft with no air resistance at all. Right now FB is at rest, high above the ground, and her sidekick Supersparrow (SS) is circling way above her. FB wants to toss a donut straight up to SS. (1) RNG: SS is 5-9 km above FB. State the random height, then calculate the minimum initial velocity the donut would need to rise straight up to SS's altitude. Be careful with units! Check: does the calculated velocity give the correct displacement? (2) Calculate how much time it would take the donut to reach SS's altitude if launched at this initial velocity. Check: put Δt back into the original expression, or a different one: do you get the right displacement? (3) RNG: Before actually throwing the donut, FB realizes that SS is going to reach the point directly above her 10-20 s sooner than the time found in #2, so the donut has to be thrown faster than that to get to SS in time. Example: if your answer to #2 was 58.3 s, you'd use the RNG button to pick a random time Δt = 38.3-48.3 s, since 58.3 s – 20 s = 38.3 s, and 58.3 s – 10 s = 48.3 s. State your new random Δt, then calculate the actual initial velocity needed to make the donut reach the same height in this time. Tip: the donut won't when it reaches SS's altitude this time – can you see why? Check: FB has to throw the donut faster than the speed calculated in #1. Now, FB launches the donut at the velocity calculated in #3, but SS misses the catch. The missed donut rises to some forever unknown maximum height, then begins falling back down again. (4) MVQ, RNG: SS chases the donut, catching up to it either when it's 2-4 km above Fastball (if the second-tolast digit of your phone number is even) or 2-4 km below Fastball (odd). State how many km above or below Fastball the donut will be caught – nothing else (no calculations). (5) Make a sketch showing the interval from launch to interception, showing • the donut at launch (beginning), and then just before interception (end) • two vectors (arrows) labeled vi, vf, showing the donut's velocity at its initial and final positions • one vector labeled a, showing the direction of the donut's acceleration during this interval • one vector labeled Δx (or Δy) showing the donut's displacement for this interval The sketch should be at least as large as your hand, so that all parts of it are easy to read online, and should have only the four vectors moentioned above. Tip: vectors aren't curved – they point in just one direction. (6) Still treating the entire flight of the donut, from launch (at the initial velocity found in #3) to just before interception, as a single interval of motion, calculate the donut's velocity the instant (before) SS catches it. This means not breaking the flight into sub-intervals. Checks: see Exam Info > Square roots. Given which direction the donut is traveling, what must be the sign of its velocity? And given where the donut is intercepted, relative to FB, should this final velocity be faster or slower than the initial velocity? (7) Calculate the donut's total flight time from launch to interception, again not breaking the flight into subintervals and solving them separately. Check: compare the calculated flight time to the partial rise time chosen in #3: which should be larger?