moderate wind accelerates a pebble over a horizontal xy plane with a constant acceleration a = (4.07 + 8.0)) m/s. At time t -0. he velocity is (4.07) m/s. What are the (a) magnitude and (b) angle of its velocity when it has been displaced by 13.0 m parallel to the xaxis? (a) Number (b) Number Units Units
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- I) (a) We will start with displacement, the straight line (as the crow or airplane flies distance) covered by a moving object starting from an initial location and arriving at a final location. Vector quantities will be written in bold face i.e. A. Consider the situation of an ant that travels east, i.e. along the x axis, for 8 cm then travels northeast, i.e. 45° from the x axis, for 11 cm. Represent each leg of this journey by a vector on your graph paper. Vectors are written as arrows with the direction going from the tail of the arrow to the head of the arrow and the length of the arrow proportional to the magnitude (size) of the vector. Indicate the first part of the journey by an arrow of length 8 cm whose tail starts at the origin of your graph and whose head is at 8 units along the positive x direction. Call this vector A which is the displacement of the first part of the ant's journey. Now starting at the head of A draw a vector B which represents the second part of the ant's…A chipmunk scampers about collecting in its cheeks safflower seeds that the birds dropped from the feeder hanging overhead. Initially, the little creature is at position vector rix = 3.49 m and r1y = -1.85 m. After filling up, it runs to the hole at position vector r2x = -1.37 m and r2y = 4.71 m that leads to its underground nest. Find component Arx of the chipmunk's displacement vector for this expedition. Arx = Find component Ary of the chipmunk's displacement vector for this expedition. Ary =0, 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) Explain
- Problem 4: A soccer ball is kicked from ground level across a level soccer field with initial velocity vector vo = 8 m/s at 0= 16° above horizontal. The soccer ball feels wind resistance which causes it to slow horizontally with constant acceleration magnitude a, = 0.54 m/s, while leaving its vertical motion unchanged. Assume any other air resistance is negligible. Choose the positive direction ofx from initial point towards final point of flight. Use a Cartesian coordinate system with the origin at the ball's initial position.h 2tar monic motron along ta- x-axis. Os c lares wi Its displacement varies wf 2 tao in seconds and仏angke in par enfees, s ale in radians. Determine the Apltude, fre reavencyA particle undergoes three consecutive displacements: and d3 = (-- 13i + 15j) cm. Find the components of the Solution Three-dimensional displacements are more diffi- + 12k) cm, d, = (23i – 14j -5.0k) cm Your final p (15i + 30j d = the origin. Despite sions, we ca resultant displacement and its magnitude. to the care for vector cult to imagine than those in two dimensions, because the latter can be drawn on paper. For this problem, let us conceb tualize that you start with your pencil at the origin of a piece of graph paper on which you have drawn x and y axes. Move your pencil 15 cm to the right along the x axis, then 30 cm upward along the y axis, and then 12 cm vertically away from the graph paper. This provides the displacement described by dj. From this point, move your pencil 23 cm to the right parallel to the x axis, 14 cm parallel to the graph paper in the -y direction, and then 5.0 cm vertically downward to- ward the graph paper. You are now at the displacement from the origin…
- The figure shows the path taken by a drunk skunk over level ground, from initial point i to final pointL The angles are 6 - 30.0o: - 51.0 and - 77.0.and the distances are dy - 440 m d - 7.10m and dy - 13.0m What are the ta) magnitude and Ibi angle of the skunk's displacement fromi to Give the ande as a positive (counterdlockwisel or negative (clockwise) angle of magnitude less than 180 measured from the direction la) Number Units (b) Number UnitsAn arrow is launched from ground level, with an initial speed of 27.2 m/s at an angle of 31.4° above the horizontal. Neglect air resistance, and take upward as the positive direction. a) How much time is needed for the arrow to reach its maximum height, b) what is this maximum heightc) how long does it take to land on the ground againd) how far does it travel right before it lands.A spider moves on a wall along the path shown in the figure. The spider's position and velocity is indicated at t; = 0 and t; = 6.00 seconds. The spider's initial velocity v; = 0.100 m/s is toward the North and final velocity vị = 0.100 m/s is toward the East. Determine the following: a) The x- and y-components of the displacement b) The x- and y-components of the average velocity c) The x- and y-components of the average acceleration. y (m) v = 0.100 m/s 0.350 = 0.100 m/s 0.150- x (m) 0.100 0.400
- A man starts walking north at 4f t/s from a point P. Five minutes later a woman starts walking southat 5f t/s from a point 500f t due east of P. At what rate are the people moving apart 15m after the womanstarts walking.#3) A soccer ball is kicked in Ritter Park such that the initial velocity vector is at 56.0 degrees angle relative to the ground and the magnitude of the initial velocity vector is 30.0 m/s. What is the time of flight of the ball and how far did it go (neglect air resistance and assume the ground is infinitely flat)? Remember, equations first, algebra, numbers last. Report answer to three sig figs.In 3.00 h a baloon drifts 21.3 km north, 8.09 km east, and 2 d285 km upward fromits release point on the ground. Find (al the magnitude of its average velocity and (b) the angle its average velocity makes with the horizontal (a) Number Units This anower has no units *(degrees (b) Number Units km km/h Hint 2 Attempts: unlimited Submit Amwer Save for Later kgmsor Ns Nim 2or Pa times