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Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
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- Q2/ The pipe in Fig. is driven by pressurized air in the tank. What is the friction factor (f) when the water flow rate through pipe is ( 85 m/hr ) and the pressure at point 1 is (2500 kPa). (25Marks) 30m smooth pipe d = 70mm open jet P1 1 90m 15m 60marrow_forwardExample 7: Rocket sleds were used to test aircraft and its effects on human subjects at high speeds. It is consisted of four rockets; each rocket creates an identical thrust T. Calculate the magnitude of force exerted by each rocket (T) for the four-rocket propulsion system shown in the Figure. The sled's initial acceleration is 49 m/s, the mass of the system is 2100 kg, and the force of friction opposing the motion is known to be 650 N. Solution: H.W Free-body diagramarrow_forwardA person places $5000 in an account that accrues interest compounded continuously. Assuming no additional deposits or withdrawals, how much will be in the account after seven years if the interest rate is a constant 8.5 percent for the first four years and a constant 9.25 percent for the last three years?arrow_forward
- 2. 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_forward4. Consider the building from the figure below. a) If it is 200 feet tall and you are 20 feet away, at what angle from the ground will you have to tilt your head to see the top of the building? (For simplicity assume that your head is even with the ground.) How far is it from your head to the top of the building? Repeat parts (a) and (b) assuming your head is NOT even with the ground, but is 6 feet above ground level. b) c) angle distance d height harrow_forwardSuppose you are driving a car at 80 miles per hour. Again decelerating at 16 feet per second squared it will take you (..............) seconds to stop. During that time you will travel(............) feet. Assuming that it takes you 1 second to react to an emergency before you start braking, at the same initial speed, and the same constant deceleration, you will travel a total of (................) feet, before coming to a stop.arrow_forward
- A simple pendulum is formed of a rope of length L = 2.2 m and a bob of mass m. %3D When the pendulum makes an angle e 10° with the vertical, the speed of the %3D bob is 2 m/s. The angular speed, e', at the lowest position is equal to: (g = 10 m/s^2)arrow_forwardI A bob attached to a cord is moved to the right where its vertical position is 1.05 cm above the equilibrium position and is then given an initial speed of 0.6 m/s. What are the values of the maximum speed and maximum height reached by the bob? (Take g = 9.8 m/s') (a) hmax (b)hmax =D1.87 cm; tnax 3.44 m/s (c) hmax (d) hmax 2.89 cm; Vnax = 0.75 m/s 1.87 cm; max 0.75 m/s 2.89 cm; 1,ax 3.44 m/s or frequency to 2/:arrow_forwardA 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5 pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5 gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows. Q' (t) = = (b) Find the quantity of salt in the tank as it's about to overflow. esc C ✓ % 1 1 a 2 W S # 3 e d $ 4 f 5 rt 99 6 y & 7 h O u * 00 8 O 1 9 1 Oarrow_forward
- 3. The equations of motion of the airplane in a straight line steady symmetrical climb are: V md- dt =T-D L-W=0 OT W siny - D= 0 L W cosy 0 V md- = T L - dt = W siny - D W cos y = 0arrow_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_forwardA window is in the form of an equilateral triangle surmounted on a rectangle. The rectangle is of clear glass and transmit twice as much light as does the triangle which is made of stained glass. If the entire window has a perimeter of 20 feet, find the dimensions of the window that will admit the most light.arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole