An ion's position vector is initially f 5.0i -6.0j+2.0k, and 10 s later it is f= -2.0 + 8.03 - 2.0k. In unit vector notation, what is its davg during the 10 s?
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- A Block-Spring System A block of mass 1.0 kg is attached to horizontal spring that has a force constant of 2,000 N/m as shown in figure (a). The spring is compressed 3.0 cm and then released from rest as in figure (b). (a) A block attached to a spring is pushed inward from an initial position x -0 by an external agent. (b) At position x, the block is released from rest and the spring pushes it to the right. x = 0 (For the following, when entering a mathematical expression, do not substitute numerical values; use variables only.) (a) Calculate the speed of the block as it passes through the equilibrium positio x = 0 if the surface is frictionle SOLUTION Conceptualize This situation has been discussed before, and it is easy to visualize the block being pushed to the right by the spring and moving with some speed at x = 0. Categorize We identify the system as the block and model the block as [--Select-- Vsystem. Analyze In this situation, the block starts with v, = 0 at x, = -3.0 cm, and…A velocity vector 49∘ above the positive x-axis has a y-component of 10 m/s. What is the value of its x-component?43.0 m above level ground at the bottom 17.5 m/s. The rock leaves his hand at a height of h A person stands at the edge of a cliff and throws a rock horizontally over the edge with a speed of vo of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the rock leaves the hand. х (a) What are the coordinates of the initial position of the rock? (Enter your answers in m.) %3D Уo 3 (b) What are the components of the initial velocity? (Enter your answers in m/s.) m/s Vox m/s Voy %D х (c) Write the equations for the x- and y-components of the velocity of the rock with time. (Use the following as necessary: t. Assume that v, and v, are in m/s and t is in seconds. Do not include units in your answers.) m/s Vx %D m/s V. II
- Find the following for path A in the Figure, measuring the displacementsfrom the back of the arrow, indicated by a dot, to the arrow's head. Round to the nearest integer. a. The distance traveled in meters. b. The magnitude of the displacement from start to finish in meters.please please help!!Problem 8: Consider two vectors A and B, expressed in unit vector notation as A= aji+ azj and B = bji+ bzj. A. Part (a) Enter an expression for the vector sum A + B in terms of quantities shown in the expressions above. A+B = B 7 8 HOME a i j k 4 5 6 a1 a2 bị 1 2 3 b2 d + END - h VO BACKSPACE CLEAR m DEL Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback. Part (b) Enter an expression for the difference vector A - B in terms of quantities shown in the expressions above. Part (c) Enter an expression for the square of the magnitude of the sum vector |A + B| in terms of quantities shown in the expressions above.
- 9. The displacement vectors A T and B shown in Figure P3.9 both have of magnitudes 3.00 m. The direction of vec- 30.0°. Find gra- tor A is 0 phically (a) А+ В, (Ь) А - В (c) B- A, and (d) A – 2B (Report all angles counterclock- wise from the positivex axis.)IT.0.0a Given an acceleration vector, initial velocity (uo.Vo), and initial position {xo.yo}, find the velocity and position vectors for t2 0. a(t) = (cos t,5 sin t. (Uo Vo) = (0,5) , (Xo.Yo) = (2.0) What is the velc | vector? v(t) =Please inlcude the complete and step-by-step soluttion. Thanks!