Free fall One possible model that describes the free fall of an object in a gravitational field subject to air resistance uses the equation v′(t) = g – bv, where v(t) is the velocity of the object for t ≥ 0, g = 9.8 m/s2 is the acceleration due to gravity, and b > 0 is a constant that involves the mass of the object and the air resistance.
a. Verify by substitution that a solution of the equation, subject to the initial condition v(0) = 0, is
b. Graph the solution with b = 0.1 s–1.
c. Using the graph in part (c), estimate the terminal velocity
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Chapter D1 Solutions
CODE/CALC ET 3-HOLE
Additional Engineering Textbook Solutions
Calculus and Its Applications (11th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus & Its Applications (14th Edition)
Glencoe Math Accelerated, Student Edition
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
- (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(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_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_forward
- M D d T M. P- A circular shaft having diameters D and d and a groove of radius r (with M = 0 and P O) is made of steel with the allowable shear stress tall. Find the maximum torque I that can be transmitted by the shaft. Given: D = 28mm, d = 20mm, r = 4mm, and tall = 250 MPa. Please help with this question. The answer should be 157.1 Nmarrow_forward13.sol Matlab The electrical circuit shown consists of resistors and voltage sources. Determine the current in each resistor, using the mesh current method that is based on Kirchhoff's second voltage law. V =38 V, V = 20V, V, = 24V R, =15Ω R, = 182 R, = 10Ω R, =9Ω R, = 5Ω R, = 14Ω R, = 82 R, = 132arrow_forwardIn matlab code Find the velocity of mars, earth, venus. In the descent phase of an extraterrestrial space mission, a spacecraft free falls through the planet's atmosphere. As it falls, it will reach a constant or terminal velocity when the air resistance force balances the gravitational attraction force. The terminal velocity is given by V₁ = where m is the spacecraft's mass [m], g is the acceleration due to gravity on the planet, p is the atmosphere's density [kg/m³], Cp is the spacecraft's drag coefficient, and A is the spacecraft's cross-sectional area [m²]. a) Write a function named terminalVelocity which calculates the terminal velocity an object. The function should . 2mg pCDA input m, g, p, CD, and A output the terminal velocity b) Write a program named q03.m which calculates the terminal velocity of a spacecraft at 10 km above the surface of various planets. The spacecraft's properties are m = 240 [kg], A= 15 [m²], and Cp = 0.5. The program should use the gravity and terminal…arrow_forward
- 3. The velocity of a particle which starts from rest is given by the following table. t see) 0 2 8 10 12 14 16 v (fusee) o 12| 16 26 40| 44 25 12 18 Evaluate using trapezium rule, the total distance travelled in 18 seconds.arrow_forwardSuppose that a parachutist with linear drag (m=50 kg, c=12.5kg/s) jumps from an airplane flying at an altitude of a kilometer with a horizontal velocity of 220 m/s relative to the ground. a) Write a system of four differential equations for x,y,vx=dx/dt and vy=dy/dt. b) If theinitial horizontal position is defined as x=0, use Euler’s methods with t=0.4 s to compute the jumper’s position over the first 40 s. c) Develop plots of y versus t and y versus x. Use the plot to graphically estimate when and where the jumper would hit the ground if the chute failed to open.arrow_forwardThe 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. SOLVE WITH MATLAB PLEASEarrow_forward
- Pyhton Help, As soon as possible You and your friend sell 80 tickets to a raffle. You sold 20 more than your friend. The goal of this problem is to find how many tickets you and your friend have sold. (a) Set up the linear equation for this problem as Ax = b, where x = number of tickets your friend sold. (b) Find A-¹ (Please show your steps). (c) Use A-¹ to solve x. (d) Use python to verify that your A-¹ and solution x are correct. Write your answers for part a here, find the Matrix A from scratch. Write your answers for part b here, please calculate A-¹ manually Write your answers for part c here, x = A-¹b, please perform this calculation manually. [] import numpy as np A = np.array(...) b = np.array(...) [] x2 Fill in the blank in the code cell below for part d, please use your own Python code to replace "..." parts. If you prefer, you can write your piece of code from scratch instead (without filling in the blanks). A_inverse = . Let x₁ represent number of tickets you sold, and x2…arrow_forwardQ1/The pressure drop in pascals (Pa) for a fluid flowing in a pipe with a sudden decrease in diameter can be determined based on the loss of head equation given below: h = 24-11 2g Area A Area A Area A Where: V₂ is the velocity in position 2 (m/s), g: is acceleration due to gravity = 9.81 m/s², A₁ and A₂ are the cross-sectional areas of the tube in position 1 and 2 respectively. A==d² Where: d is the diameter (m). Write a program in a script file that calculates the head loss. When the script file is executed, it requests the user to input the velocity (V₂) in m/s and values of diameters (d, and d₂). The program displays the inputted value of v followed by a table with the values of diameters in the first and second columns and the corresponding values of h, in the third column. 2 2arrow_forwardDraw a CIRCLE OF UNIT RADIUS: Use parametric equation of unit circle x=cos , y= sin 0arrow_forward
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr
![Text book image](https://www.bartleby.com/isbn_cover_images/9781133187844/9781133187844_smallCoverImage.gif)