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12-D13 The roller coaster starts at point A with a speed of 4 m/s and a tangential acceleration of a = (5-0.29 m/s2. when s=10m, x=20m at point B. y = .008x2 At B, determine the velocity, normal acceleration, tangential acceleration, and total acceleration. Sketch the acceleration vectors on the picture.
4) (16 points) The function f(x)= x? – 2x² - 4x+8 has a double root at x = 2. Use a) the standard Newton-Raphson, b) the modified Newton-Raphson to solve for the root at x = 2. Compare the rate of convergence using an initial guess of Xo = 1,2. 5) (14 points) Determine the roots of the following simultaneous nonlinear equations using a) fixed-point iteration and b) the Newton-Raphson method: y=-x? +x+0,75 y + 5xy = r? Employ initial...
A bowling ball of mass 7.5 kg and diameter 18 cm rolls without skipping down a 10-m bowling lane with a constant speed 4.3 m/s. A. Through what angle does the bowling ball turn as it travels the length of the lane? B. What is the angular speed of the bowling ball? C. Calculate the maximum radial acceleration that a point in the surface of the bowling ball could have. D. Calculate the tangential acceleration of a point on the...
6. General Motion with Unit Vectors and Components An object undergoes the following consecutive displacements: s (2i +3j +5k)m,s2 (6i- 9j + 2k)m, and s3 (10i 8j -k)m. a) Find the resultant displacement in terms of unit vectors and components. b) State the magnitude of the resultant displacement. 2. Suppose a hiker travels 5 km southwest from their camp. Then, the hiker travels 2 km 75° north of east. a) Find the displacement of the hiker form their camp. b)...
Q1 (b) A truck A pulls a crate B up a slope that is inclined at an angle of 150 to the horizontal, as shown in Figure Q1(b). The rope passes over a pulley of negligible size at C. At the instant shown, r 30 m, 0-45o and the truck has a speed of vA 20 km/h and an acceleration ax-0.2 m/s i) Express the velocity components of the crate B along the rope (4 marks) BC and transverse to...
Which of the following statements about f(x) are true given that f′(x)=2x^3−4x^2? f(x) has a point of inflection at x=0 and minima at x=2. f(x) has a point of inflection at x=1 and minima at x=2. f(x) has a maxima at x=0, and a minima at x=2. f(x) has a point of inflection at x=0 and minima at x=3
Rolling a ball requires which of the following: 1. centripital acceleration 2. inear velocity 3. constant speed 4. static friction (more than one may apply)
A batter hits a baseball 3 feet above the ground toward the center field fence, which is 10 1. feet high and 400 feet from home plate (where the batter stands when he hits the ball). The bal leaves the bat with a speed of 115 ft/s at an angle of 50° above the horizontal. Is it a home run? That is, does the ball clear the fence? You do not need to derive the formulas for projectile motion from...
4. General Motion with Unit Vectors and Components An object undergoes the following consecutive displacements: s (2i +3j +5k)m,s2 (6i- 9j + 2k)m, and s3 (10i 8j -k)m. a) Find the resultant displacement in terms of unit vectors and components. b) State the magnitude of the resultant displacement. 2. Suppose a hiker travels 5 km southwest from their camp. Then, the hiker travels 2 km 75° north of east. a) Find the displacement of the hiker form their camp. b)...
5. General Motion with Unit Vectors and Components An object undergoes the following consecutive displacements: s (2i +3j +5k)m,s2 (6i- 9j + 2k)m, and s3 (10i 8j -k)m. a) Find the resultant displacement in terms of unit vectors and components. b) State the magnitude of the resultant displacement. 2. Suppose a hiker travels 5 km southwest from their camp. Then, the hiker travels 2 km 75° north of east. a) Find the displacement of the hiker form their camp. b)...