Conservation of energy A projectile with mass m is launched into the air on a parabolic trajectory. For t ≥ 0, its horizontal and vertical coordinates are x(t) = u0 t and
Use the Chain Rule to compute
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
- A simple pendulum of length L, has a maximum angular displacement e_max. At one point in its motion, its kinetic energy is K = 3 J and its potential energy is U = 4.2 J. When the pendulum's angular velocity is one-fourth its maximum value (0' = %3D O'_max/4), then its kinetic energy is:arrow_forwardA circle in the XY-coordinate system is specified by the center coordinates (x, y) and radius (r). Read the values for 2 circles- x1, y1, r1 for C1 and x2, y2, r2 for C2. (i) Determine whether the 2 circles intersect. To solve the problem it suffices to check if the distance between the 2 centers is lesser than the sum of radii of the 2 circles. (ii) Find the smallest circle that encloses the two circles and return its center coordinates and radius. programming language - carrow_forwardThe spring in the figure below is stretched from its equilibrium position at x = 0 to a positive coordinate xo. ko HINT x = 0 x = xo PE sn PE 50 The force on the spring is F and it stores elastic potential energy PESO. If the spring displacement is tripled to 3x, determine the ratio of the new force to the original force, and the ratio of the new to the original elastic potential energy, Fo Fo PESO (a) the ratio of the new force to the original force, PE ST PE SO (b) the ratio of the new to the original elastic potential energy,arrow_forward
- INTRODUCTION: Heat conduction from a cylindrical solid wall of a pipe can be determined by the follow T1-T2 q = 2nLk R2 In R. where: q is the computed heat conduction in Watts. k is the thermal conductivity of the pipe material in Watts/°C/m. L is the length of the pipe in cm. Ri is the inner radius of the pipe in cm. R2 is the outer radius of the pipe in cm. Ti is the internal temperature in °C. T2 is the external temperature in °C. ASSIGNMENT: Write a C program that will allow the user to enter the inner and outer radii of the pipe, the the internal and external temperatures. Once the user enters the input values, the programarrow_forward(Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a cylinder, this moment of inertia is given by this formula: J=mr2/2+m( l 2 +3r 2 )/12misthecylindersmass( kg).listhecylinderslength(m).risthecylindersradius(m). Using this formula, determine the units for the cylinder’s polar moment of inertia.arrow_forward(Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.arrow_forward
- The electric flux density D at the point M (0,4,0) in the region about a uniform line charge of 1 nC/m lying along the z axis in free space is: Select one: a. None of the above b. 0.6366 nC/m c. 0.2387 nC/m d. 0.039 nC/m e. 0.1 nC/marrow_forwardThe van der Waal's equation of state is given as RT a v-b v² For sulfur dioxide at temperature, T, of 300 K and a pressure, P, of 1 atm, the constants are given as: R = 0.08206 L.atm/(mol.K) L2.mol² P = a = 6.7689 atm.L b=0.05679 L.mol™¹ a) Plot the function f(v)=0 the for volumes for the range of 0 to 40 L/mol using 0.5 increment. b) Identify the root in this plot (where the curve crosses x-axis). c) Use the MATLAB function (fzero) to solve the original f(v) function for the specific volume using the initial guess from part (c). d) Use the MATLAB function (roots) to solve the original f(v) function for the specific volume.arrow_forwardA discharge factor is a ratio which compares the mass flow rate at the end of a channel or nozzle to an ideal channel or nozzle. The discharge factor for flow through an open channel of parabolic cross-section is: K = 1.2 [V16x +1+ In(V16x² +1+4x)]³ 4x where x is the ratio of the maximum water depth to breadth of the channel at the top of the water. Determine the discharge factors for x in the range 0.45 to 0.90 in steps of 0.05. Script e C Reset I MATLAB Docume 1 %Give values for x: 2 3 %Solve for K: 4arrow_forward
- During a journey, a car accelerates from (10 m/s) to (20 m/s) in (5 sec). Calculate the acceleration of the car: 2.5 О 3.0 1.5 2.0 A bullet of mass 20g is found to pass two points 30m apart in a time interval of 4s. Calculate the kinetic energy of the bullet if it moves with constant speed. * 0.562J O 5J 2J O 2.5Jarrow_forward2. The flight of a model rocket can be modeled as follows. During the first 0.15 s the rocket is propelled upward by the rocket engine with a force of 16 N. The rocket then flies up while slowing down under the force of gravity. After it reaches the apex, the rocket starts to fall back down. When its downward velocity reaches 20 m/s, a parachute opens (assumed to open instantly), and the rocket continues to drop at a constant speed of 20 m/s until it hits the ground. Write a program that calculates and plots the speed and altitude of the rocket as a function of time during the flight.arrow_forwardf (x) = -x2+ 8x - 12 Determine the maximum and the corresponding value of x using: Newton’s method (x0 = 2, iterations = 3).arrow_forward
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr