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- A hiker walks from (x1, y1) = (4.00 km. 3.00 km) to (x2, y2) = (3.00 km, 6.00 km), (a) What distance has the traveled? (b) The hiker desires to return to his starting point. In what direction should he go? (Give the angle with respect to due cast.) (See Sections 3.2 and 3.3.)arrow_forwardA particle moves along the x axis according to the equation x = 2.00 + 3.00t 1.00t2, where x is in meters and t is in seconds. At t = 3.00 s, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.arrow_forwardConsider a projectile launched at a height h feet above the ground and at an angle 0 with the horizontal. If the initial velocity is v, feet per second, the path of the projectile is modeled by the parametric equations x = t(vo cos(0)) and y = h + (vo sin 0)t - 16t2. A rectangular equation for the path of this projectile is y = 7 + x - 0.008x². (a) Eliminating the parameter t from the position function for the motion of a projectile to shows that the rectangular equation is as follows. -16 (sec(0))2 y = x² + tan(0)x + h Vo (b) Find h, vo, and 0. (Round your answers to two decimal places.) Vo %3D (c) Use a graphing utility to graph the rectangular equation for the path of the projectile. Confirm your answer in part (b) by sketching the curve represented by the parametric equations. 60 50 40 30 20 50 100 150 10 50 100 150 60 50 60 50 40 40 30 30 20 10 50 100 150 10 20 40 60 80 (d) Use a graphing utility to approximate the maximum height of the projectile. (Round your answers to two…arrow_forward
- Vectors u = −10i + 3j and v = −7i − 9j. What is u − v? a −17i − 6j b 17i + 6j c 3i − 12j d −3i + 12jarrow_forwardA space shuttle’s coordinates as functions of time are given by x(t) = 7.0 t^3 and y(t) = 4.0t^2 - 2.1t , where x and y are in meters and t is in seconds. write a vector expression for the ball's position as a function of time.arrow_forwardAn aeroplane moves so that at time t seconds, its position vectors, r metres, is given by: r= (40t)i + (3r² + 201) j The unit vectors i and j are that are directed horizontally and vertically respectively. The aeroplane is initially at ground level. a) Find the time when the height of the aeroplane is 500 metres. ( seconds) b) Find the speed of the aeroplane at this time. ( m/s) c) Find the magnitude of acceleration of the aeroplane. ( m/s2)arrow_forward
- The initial velocity of a car, v i is 45 km/hr in the positive x-direction. The final velocity of the car, vf is 66 km/hr in a direction that points 750 above the positive x-axis. Sketch the vectors v = v f − v i . Find the magnitude of the change in velocity v. Find the direction of the change in velocity v.arrow_forwardthe coordinates of an object moving in an xy plane vary with the time according to the eqations x=-7.85 sin w(omega)t, and y=4-7.85 cosw(omega)t. W(omega) is constant , x,y - in meters. And t in seconds. Write expressions for the possition,velocity and acceleration vectors of the object at any time t>0.arrow_forwardA golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x = 17.0t and y = 4.20t − 4.90t2, where x and y are in meters and t is in seconds. (a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and ĵ. (Give the answer in terms of t.) = m By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector as a function of time = m/s(c) obtain the expression for the acceleration vector as a function of time = m/s2(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.24 s. = m = m/s = m/s2arrow_forward
- A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x = 19.4t and y = 4.04t - 4.90t2, where x and y are in meters and t is in seconds. (a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and j. (Give the answer in terms of t.) F = m By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector v as a function of time マ= m/s (c) obtain the expression for the acceleration vector a as a function of time m/s? (d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 2.94 s. = m/s a = m/s2arrow_forwardA golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x=18.0t and y=4.00t−4.90t 2 , where x and y are in meters and t is in seconds. (a) Write a vector expression for the balls position as a function of time, using the unit vectors i^ and j^ . By taking derivatives, obtain expressions for (b) the velocity vector v as a function of time and (c) the acceleration vector a as a function of time. (d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t=3.00s.arrow_forwardThe position vector 4.70t|i+ [et + ft2 locates a particle as a function of time t. Vector is in meters, t is in seconds, and factors e and f are constants. The figure gives the angle e of the particle's direction of travel as a function of time (0 is measured from the positive direction of the x axis). What are (a) factor e and (b) factor f, including units? 20° 0° 10 20 -20° t (s) (a) Number Units (b) Number Unitsarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning