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(III) The position of a particle moving in the xy plane is given by
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- The position r of a particle moving in an xy plane is given by ř seconds. In unit-vector notation, calculate (a) 7, (b) V , and (c) a for t = 3.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 3.00 s? Give your answer in the range of (-180°; 180°). (4.00r3 – 1.00t)î + (5.00 – 1.00r4)j with 7 in meters and t in (a) Number i i Units (b) Number ît i Units i (c) Number i i Units (d) Number i Unitsarrow_forward0, y 0) 44. A projectile is launched from the point (x QC with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance |r| from the ori- gin at the end of each second thereafter, for 0 s I S 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v and v will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to f, then r|must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explainarrow_forwardThe position of a particle moving in the xy plane varies with time, and its coordinates are given by the following expressions: x(t) = 4.00 m +r cos[(4.00/s)t] and y(t) = r sin[(4.00/s)t], where r = 2.00 m, and x and y will be in meters when t is in seconds. Determine the following for this particle. (a) speed of the particle at any time m/s (b) magnitude of the acceleration of the particle at any time m/s?arrow_forward
- (b) A particle moves with position y = 2x , where x and y are in meters. The velocity in x direction is v, = 31² . Determine the velocity at time t = 5 s and write in unit vectors.arrow_forward22)))At t = 0, a particle moving with constant acceleration in the xy plane has a velocity v = (3.00i-2.00j) m / s at its origin. At t = 3.00 s, the velocity of the particle is v = (9.00i + 7.00j) m / s. Find the acceleration of the particle?arrow_forwardThe position of a particle is given by r(t) = A (cos wt i + sin wt j ). where w is a constant. (a) Show that the particle moves in a circle of radius A.arrow_forward
- The position F of a particle moving in an xy plane is given by: F =(2.00"–5.00t)i +(6.00–7.00€*)} with ř in meters and t in seconds. (Note that this is an example where the units for the coefficients are ignored – don't let this distract you!) In unit vector notation, calculate: а). г b). V с). а for time t = 2.00 s. d). What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t= 2.00 s?arrow_forwardA projectile is launched from the point (x = 0, y = 0), with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance T from the ori- gin at the end of each second thereafter, for 0 < t s 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v, and v, will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to r, then r must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain your method for solving part (c).arrow_forwardQuestion 5: The position vector of a particle moving in a circular path of radius R is given by the following expression T(t) = R[– sin(3t²)î+ cos(3t²)3] where B is a positive constant (i and j are the unit vectors corresponding to x and y axes in the two dimensional Cartesian Coordinate System, respectively). At time t = 4 secs., what is the ratio of magnitudes of the tangential acceleration and the centripetal acceleration, at where at and aț are the magnitudes of the tangential and the centripetal accelerations, respectively.arrow_forward
- Initially, an object in uniform circular motion (assume clockwise motion) has a velocity vector given by v = (-3.00") î + (4.00"). If the radius of travel is 3.00 meters, determine the acceleration vector (in unit-vector notation) after 5.00 seconds have elapsed.arrow_forward(e) Calculate for a 14 m/s turn of radius 28 m. Assume all quantities are correct to 3 significant figures. Enter to 3 significant figures 0= ✔degreesarrow_forwardA car P travels along a straight road with a constant speed v = 55 mi/hr. At the instant when the angle θ = 62°, determine the rate at which the angle θ varies with time (rad/sec) if d=84ft. Round off only on final answer expressed in three decimal places.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill