Use these formulas to help you solve the problems below.

Chapter 1: This chapter was setting up the math. Familiarity with vectors is big here A . B = B . A = |AB|cos(0) | A . B = Ar Br + Ay By + AB, I AXB - -BX A = AB sin(0) | Ax B = (A,B, - A,By )it (A,Br - A.B. ) j + (A,By - AB.) k Chapter 2: Gradients are for variables that dont change with time, derivatives are for variables that change with time = TitUrAt|v. = 12 At IAc = fy vdt | a = du Uf = vi + aAt |xf = x; + viAt + zant | (of )? = (v; )2 + 2ax Chapter 3: Several topics didn't have equations, like reference frames and some directions of relative velocity. Its worth looking those parts over. Ar = (Ax)i + (Ay)y = Tri tryj | Ar = rf - ~x = ut+ x lung # 10= E dy dt AT aavg la = du At At dt | Range = " sin(20) |a. = "plac = " = w'rcs from Slides: Here are several still images from slides of different useful equations. 1D Motion Physics is Calculus S position V velocity a acceleration time ..... differentiate differentiate S integrate a integrate V= # S=0 V=0 a=0 particle is particle is: . momentarily at rest particle is at the origin . instantaneously at rest at constant velocity . stationary . changing directions ds : Minimum/ position set -=0, solve for f, plug back into S Maximum dv velocity set - = 0, solve for f, plug back into v yf = VitV Al+= aAtz Vyf = Vita, At 2=v z+ 2a Ay x, = X, + V At+ - a, At- 2' Vxf = Vita, At 2=V.- +2a,Axdisplacement Ax= X f - X; Kinematics Equations (constant acceleration) Ax = V.; + a At average velocity VE V xf At Xf = X; +VAt+-a,At2 1 total distance 2 average speed total time (v (v. )' + 2a, Ax instantaneous velocity dx V E dt Free Fall instantaneous speed Vx On Earth, when not touching anything, objects fall due to Av average acceleration a= Vf Vi gravity towards the Earth's At if - t ; center with acceleration: dv instantaneous acceleration d' x g= 9.80 m/s2 a= = dt dt2 (neglecting air resistance)\fAngular speed does not depend on radius linear angular position Ax do velocity V= W = dt dt dw acceleration a = Of = dt dt Galilean Transformations Position x = x'tvt x'= x- vI y = y+VI y'= y-VI E'-E-VI S velocity measured in s' velocity velocity measured in s u' = u - V u = utv velocity of s' relative to sT. (10 points) Arya, my little black and white cat that those who attended office hours have seen, has a giant hamster wheel she runs on. Assume she starts from rest, and the wheel rotates on perfectly frictionless supports. The wheel's inner diameter is 1 meter. a) If Arya accelerates the wheel at a constant angular acceleration of 7.5 radr's2 for 3 seconds, what is the final angular speed of the wheel? b) What is Arya's tangential speed, in relation to the hamster wheel. afterthe 3 seconds? c) What is Arya's centripetal acceleration, when running at full speed (after the 3 second duration) on the bottom of the hamster wheel? 8. (10 Points) Vin, an allomancer {e.g. magicy person) from the Mistborn trilogy (Era 1): has a number of innate powers. One ofthese is the ability to push or pull on metals from a distance. Say that \ sees an enemy allomancer on a balcony. The building is 8.0 meters horizontally from her, and the balcony is 5.0 meters high. She grabs a metal coin, and from a height of 1.0 meters above the ground, pushes (launches) the coin at the allomancer. After the push, only gravity acts on the coin. The enemy, sensing the shot, drops straight down from the balcony the instant the coin launches. Ignore air resistance. him 'rajertrory /' . a) At what angle is Vin initially shooting at? -\\:- :-:r.-m m t. _ ./ Auluaal lialaulu'y / 6W b) If the coin initially travels along that angle at 26.0 [Tl-"S, how much time passes between the coin being pushed and it arriving at the building? 8 in c) How far will the enemy allomancer fall in the time found above? Ignore air resistance. and treat the enemy allomancer as being in free fall. d) At what height will the coin hit the building? Does W1 hit hertarget