A particle starts at the point P = (7, −7, −3) and moves along a straight line toward Q = (8, −9, 0) at a speed of 5 cm/sec. Let x, y, z be measured in centimeters and t be measured in seconds. (a) Find the particle's velocity vector. v(t): = (b) Find parametric equations for the particle's motion. x(t) y(t) = z(t) = = =

A particle starts at the point P = (7, −7, −3) and moves along a straight line toward Q = (8, −9, 0) at a speed of 5 cm/sec. Let x, y, z be measured in centimeters and t be measured in seconds. (a) Find the particle's velocity vector. v(t): = (b) Find parametric equations for the particle's motion. x(t) y(t) = z(t) = = =

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 69P: A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0...

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A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69
If , and , find the unknown constants a and b such that .
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PROBLEM 1: A surveyor walks as shown in the figure then due south for 10.0km. What is his total displacement from his starting point if you measure the distance along a straight line?( N > E w 3 25 km PROBLEM 2: Find the angle between the lines given by the equations: y = 2 x +4 and y = x+ 3. 2.
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You receive orders to sail due east for 24.6 mi to put your salvage ship directly over a sunken pirate ship. However, when your divers probe the ocean floor at that location and find no evidence of a ship, you radio back to your source of information, only to discover that the sailing distance was supposed to be 24.6 nautical miles, not regular miles. Use the Length table below to calculate how far horizontally you are from the pirate ship. Length cm МЕTER km in. ft mi 1 centimeter = 1 102 105 0.3937 3.281 x 102 6.214 × 106 1 METER = 100 1 103 39.37 3.281 6.214 x 104 1 kilometer = 10° 1000 1 3.937 x 104 3281 0.6214 1 inch =2.540 2.540 x 102 2..540 × 105 1 8.333 x 102 1.578 × 105 1 foot = 30.48 0.3048 3.048 × 104 12 1 1.894 x 10* 1 mile = 1.609 x 105 1609 1.609 6.336 x 104 5280 1 1 angström = 10-10 1 fermi = 1015 m 1 fathom = 6 ft 1 rod = 16.5 ft m 1 nautical mile = 1852 m 1 light-vear = 9.461 × 1012 km 1 Bohr radius = 5.292 x 101" m 1 mil = 10* in. = 1.151 miles = 6076 ft 1 parsec =…
The equation r(t) = ( sin t)i + ( cos t)j + (t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. π Then write the particle's velocity at t= as a product of its speed and direction. The velocity vector is v(t) = (i+j+ k.
The path traveled by an object (neglecting air resistance) that is projected at an initial height of h feet, an initial velocity of v feet per second, and an initial angle is given by 16 -x² + (tan(0))x + ho v² cos²(e) where the horizontal distance x and the vertical distance y are measured feet. Find a formula for the maximum height of an object in feet projected from ground level at velocity v and angle . To do this, find half of the horizontal distance ² sin(20) 32 and then substitute it for x in the model for the path of a projectile (where h = 0).