Description: Conceptual questions about projectile motion and some easy calculations. (uses applets)

Transcription

1 Week 3: Chapter 3 [ Edit ] Overview Suary View Diagnotic View Print View with Anwer Week 3: Chapter 3 Due: 11:59p on Sunday, February 8, 2015 To undertand how point are awarded, read the Grading Policy for thi aignent. Introduction to Projectile Motion Decription: Conceptual quetion about projectile otion and oe eay calculation. (ue applet) Learning Goal: To undertand the baic concept of projectile otion. Projectile otion ay ee rather coplex at firt. However, by breaking it down into coponent, you will find that it i really no different than the one dienional otion that you have already tudied. One of the ot often ued technique in phyic i to divide two and three dienional quantitie into coponent. For intance, in projectile otion, a particle ha oe initial velocity v. In general, thi velocity can point in any direction on the xy plane and can have any agnitude. To ake a proble ore anagable, it i coon to break up uch a quantity into it x coponent and it y coponent. v x v y v degree Conider a particle with initial velocity that ha agnitude 12.0 and i directed 60.0 above the negative x axi. v x What i the x coponent of? Expre your anwer in eter per econd. v v x = 6.00 What i the y coponent of? Expre your anwer in eter per econd. v y v v y = 10.4 Breaking up the velocitie into coponent i particularly ueful when the coponent do not affect each other. Eventually, you will learn about ituation in which the coponent of velocity do affect one another, but for now you will only be looking at proble where they do not. So, if there i acceleration in the x direction but not in the y direction, then the x coponent of the velocity will change, but the y coponent of the velocity will not. 1/17

2 Part C Look at thi applet. The otion diagra for a projectile i diplayed, a are the otion diagra for each coponent. The x coponent otion diagra i what you would get if you hined a potlight down on the particle a it oved and recorded the otion of it hadow. Siilarly, if you hined a potlight to the left and recorded the particle' hadow, you would get the otion diagra for it y coponent. How would you decribe the two otion diagra for the coponent? Both the vertical and horizontal coponent exhibit otion with contant nonzero acceleration. The vertical coponent exhibit otion with contant nonzero acceleration, wherea the horizontal coponent exhibit contant velocity otion. The vertical coponent exhibit contant velocity otion, wherea the horizontal coponent exhibit otion with contant nonzero acceleration. Both the vertical and horizontal coponent exhibit otion with contant velocity. A you can ee, the two coponent of the otion obey their own independent kineatic law. For the vertical coponent, there i an acceleration downward with agnitude g = Thu, you can calculate the vertical poition of the particle at any tie uing the tandard kineatic equation y = y 0 + v 0 t + (1/2)at 2. Siilarly, there i no acceleration in the horizontal direction, o the horizontal poition of the particle i given by the tandard kineatic equation x = x 0 + v 0 t. Part D t g 2 How long doe it take for the ball to reach the ground? Ue 10 for the agnitude of the acceleration due to gravity. Expre your anwer in econd to two ignificant figure. Hint 1. How to approach the proble t = 0 The ball are releaed fro ret at a height of 5.0 at tie. Uing thee nuber and baic kineatic, you can deterine the aount of tie it take for the ball to reach the ground. t g = 1.0 Thi ituation, which you have dealt with before (otion under the contant acceleration of gravity), i actually a pecial cae of projectile otion. Think of thi a projectile otion where the horizontal coponent of the initial velocity i zero. Part E Iagine the ball on the left i given a nonzero initial peed in the horizontal direction, while the ball on the right continue to fall with zero initial velocity. What horizontal peed v x ut the ball on the left tart with o that it hit the ground at the ae poition a the ball on the right? Reeber that the two ball are releaed, tarting a horizontal ditance of 3.0 apart. 2/17

3 Expre your anwer in eter per econd to two ignificant figure. Hint 1. How to approach the proble Recall fro that the horizontal coponent of velocity doe not change during projectile otion. Therefore, you need to find the horizontal coponent of velocity v x uch that, in a tie t g = 1.0, the ball will ove horizontally 3.0. You can aue that it initial x coordinate i x 0 = 0.0. v x = 3.0 You can adjut the horizontal peed in thi applet. Notice that regardle of what horizontal peed you give to the ball, they continue to ove vertically in the ae way (i.e., they are at the ae y coordinate at the ae tie). Exercie 3.8 Decription: A reote controlled car i oving in a vacant parking lot. The velocity of the car a a function of tie i given by upilon_vec = (5.00 () ( ()^3 )t^2 )i_unit + (2.00 ()+(0.550 ()^2 )t)j_unit. (a) What i a_x(t) the x coponent... A reote controlled car i oving in a vacant parking lot. The velocity of the car a a function of tie i given by υ = [5.00 ( ) t 2 ] i^ + [ ( )t] j^. What i a x (t) the x coponent of the acceleration of the car a function of tie? a x (t) = ( )t a x (t) = ( )t a x (t) = ( )t What i a y (t) the y coponent of the acceleration of the car a function of tie? a y (t) = a y (t) = a y (t) = ( )t 3/17

4 Part C What i the agnitude of the velocity of the car at t = 7.12? Expre your anwer to three ignificant figure and include the appropriate unit. v = = 7.19 Part D What i the direction (in degree counterclockwie fro +x axi) of the velocity of the car at t = 7.12? Expre your anwer to three ignificant figure and include the appropriate unit. θ v = = 55.4 Part E What i the agnitude of the acceleration of the car at t = 7.12? Expre your anwer to three ignificant figure and include the appropriate unit. a = = Part F What i the direction (in degree counterclockwie fro +x axi) of the acceleration of the car at t = 7.12? Expre your anwer to three ignificant figure and include the appropriate unit. θ = = 115 a Exercie 3.9 Decription: A phyic book lide off a horizontal table top with a peed of v. It trike the floor after a tie of t. Ignore air reitance. (a) Find the height of the table top above the floor. (b) Find the horizontal ditance fro the edge of the table to /17

5 A phyic book lide off a horizontal table top with a peed of It trike the floor after a tie of Ignore air reitance. Find the height of the table top above the floor. y = = Find the horizontal ditance fro the edge of the table to the point where the book trike the floor. x = = Part C Find the horizontal coponent of the book' velocity jut before the book reache the floor. v x = = 1.25 Part D Find the vertical coponent of the book' velocity jut before the book reache the floor. v y = = 3.72 Part E Find the agnitude of the book' velocity jut before the book reache the floor. v = = /17

6 Part F Find the direction of the book' velocity jut before the book reache the floor. Expre your anwer a an angle eaured below the horizontal θ = = 71.4 below the horizontal Exercie 3.11 Decription: Two cricket, Chirpy and Milada, jup fro the top of a vertical cliff. Chirpy jut drop and reache the ground in t, while Milada jup horizontally with an initial peed of v_0. (a) How far fro the bae of the cliff will Milada hit the ground? Two cricket, Chirpy and Milada, jup fro the top of a vertical cliff. Chirpy jut drop and reache the ground in 3.70, while Milada jup horizontally with an initial peed of c How far fro the bae of the cliff will Milada hit the ground? x = = 3.40 Exercie 3.12 Decription: A rookie quarterback throw a football with an initial upward velocity coponent of v_y0 and a horizontal velocity coponent of v_x0. Ignore air reitance. (a) How uch tie i required for the football to reach the highet point of the trajectory?... A rookie quarterback throw a football with an initial upward velocity coponent of 16.2 and a horizontal velocity coponent of Ignore air reitance. How uch tie i required for the football to reach the highet point of the trajectory? Expre your anwer uing three ignificant figure. t 1 = = /17

7 How high i thi point? Expre your anwer uing three ignificant figure. h = = 13.4 Part C How uch tie (after it i thrown) i required for the football to return to it original level? Expre your anwer uing three ignificant figure. t 2 = = 3.31 Part D How doe thi copare with the tie calculated in part (a). Expre your anwer uing three ignificant figure. t 2 t 1 = 2.00 Part E How far ha it traveled horizontally during thi tie? Expre your anwer uing three ignificant figure. x = = 62.5 Exercie 3.28 Decription: The radiu of the earth' orbit around the un (aued to be circular) i 1.50 * 10^8 (k), and the earth travel around thi orbit in 365 day. (a) What i the agnitude of the orbital velocity of the earth in? (b) What i the radial... The radiu of the earth' orbit around the un (aued to be circular) i thi orbit in 365 day k, and the earth travel around 7/17

8 What i the agnitude of the orbital velocity of the earth in? What i the radial acceleration of the earth toward the un? Part C What i the agnitude of the orbital velocity of the planet Mercury (orbit radiu, orbital period = 88.0 day)? = k Part D What i the radial acceleration of the Mercury? Exercie 3.29 Decription: A Ferri wheel with radiu 14.0 i turning about a horizontal axi through it center (the figure ). The linear peed of a paenger on the ri i contant and equal to v. (a) What i the agnitude of the paenger' acceleration a he pae... A Ferri wheel with radiu 14.0 i turning about a horizontal axi through it center (the figure ). The linear peed of a paenger on the ri i contant and equal to /17

9 What i the agnitude of the paenger' acceleration a he pae through the lowet point in her circular otion? a = = What i the direction of the paenger' acceleration a he pae through the lowet point in her circular otion? toward the center outward the center Part C What i the agnitude of the paenger' acceleration a he pae through the highet point in her circular otion? a = = Part D What i the direction of the paenger' acceleration a he pae through the highet point in her circular otion? 9/17

10 toward the center outward the center Part E How uch tie doe it take the Ferri wheel to ake one revolution? T = = 11.1 Exercie 3.34 Decription: Two pier, A and B, are located on a river: B i 1500 downtrea fro A. Two friend ut ake round trip fro pier A to pier B and return. One row a boat at a contant peed of 4.00 k/h relative to the water; the other walk on the hore at a... Two pier, A and B, are located on a river: B i 1500 downtrea fro A. Two friend ut ake round trip fro pier A to pier B and return. One row a boat at a contant peed of 4.00 k/h relative to the water; the other walk on the hore at a contant peed of The velocity of the river i 2.80 in the direction fro to. k/h k/h A B 10/17

11 How uch tie doe it take the walker to ake the round trip? Expre your anwer uing two ignificant figure. t = 45 in How uch tie doe it take the rower to ake the round trip? Expre your anwer uing two ignificant figure. t = 88 in Exercie 3.38 Decription: An airplane pilot wihe to fly due wet. A wind of v_w i blowing toward the outh. (a) If the airpeed of the plane (it peed in till air) i v_a, in which direction hould the pilot head? (b) What i the peed of the plane over the ground? k/h An airplane pilot wihe to fly due wet. A wind of 82.0 i blowing toward the outh. k/h If the airpeed of the plane (it peed in till air) i 310.0, in which direction hould the pilot head? Expre your anwer a an angle eaured north of wet. 11/17

12 θ = = 15.3 north of wet What i the peed of the plane over the ground? v = = 299 k/h Proble 3.52 Decription: A ovie tuntwoan drop fro a helicopter that i 30.0 above the ground and oving with a contant velocity whoe coponent are 10.0 upward and 15.0 horizontal and toward the outh. You can ignore air reitance. (a) What i the... A ovie tuntwoan drop fro a helicopter that i 30.0 above the ground and oving with a contant velocity whoe coponent are 10.0 upward and 15.0 horizontal and toward the outh. You can ignore air reitance. What i the horizontal ditance(relative to the poition of the helicopter when he drop) at which the tuntwoan hould have placed the foa at that break her fall? x = 55.5 Draw x t graph of her otion. 12/17

13 Part C Draw y t graph of her otion. 13/17

14 Part D Draw v x t graph of her otion. Part E Draw v y t graph of her otion. 14/17

15 Proble 3.56 Decription: A a hip i approaching the dock at 45.0 c, an iportant piece of landing equipent need to be thrown to it before it can dock. Thi equipent i thrown at 15.0 at 60.0 degree() above the horizontal fro the top of a tower at the edge of... c A a hip i approaching the dock at 45.0, an iportant piece of landing equipent need to be thrown to it before it can dock. Thi equipent i thrown at 15.0 at 60.0 above the horizontal fro the top of a tower at the edge of the water, 8.75 above the hip' deck (the figure.) For thi equipent to land at the front of the hip, at what ditance D fro the dock hould the hip be when the equipent i thrown? Air reitance can be neglected. 15/17

16 D = 25.5 Proble 3.68 Decription: A rock i thrown fro the roof of a building with a velocity v_0 at an angle of alpha_0 fro the horizontal. The building ha height h. You can ignore air reitance. (a) Calculate the agnitude of the velocity of the rock jut before it trike the... A rock i thrown fro the roof of a building with a velocity v 0 at an angle of α 0 fro the horizontal. The building ha height h. You can ignore air reitance. Calculate the agnitude of the velocity of the rock jut before it trike the ground. v = Proble 3.81 Decription: An airplane pilot et a copa coure due wet and aintain an airpeed of v. After flying for a tie of t, he find herelf over a town a ditance x wet and a ditance y outh of her tarting point. (a) Find the agnitude of the wind velocity.... k/h h k k An airplane pilot et a copa coure due wet and aintain an airpeed of 223. After flying for a tie of 0.520, he find herelf over a town a ditance 119 wet and a ditance 20 outh of her tarting point. Find the agnitude of the wind velocity. v = = 38.9 k/h Find the direction of the wind velocity. Expre your anwer a an angle eaured outh of wet 16/17

17 θ = = 81.4 outh of wet Part C k/h k/h If the wind velocity i 39 due outh, in what direction hould the pilot et her coure to travel due wet? Ue the ae airpeed of 223. Expre your anwer a an angle eaured north of wet θ = = 10.1 north of wet Copyright 2015 Pearon. All right reerved. Legal Notice Privacy Policy Periion 17/17