Solve this Problem in Jupyter Notebook 2. Use of SciPy must be demonstrated in your solution 3. Use of latex to format numbers, variables and equations 4. Use of matplotlib for graphing
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1. Solve this Problem in Jupyter Notebook
2. Use of SciPy must be demonstrated in your solution
3. Use of latex to format numbers, variables and equations
4. Use of matplotlib for graphing
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- 1. A 500-liter tank initially contains 10 g of salt dissolved in 200 liters of water. Starting at to = 0, water that contains 1/4 g of salt per liter is poured into the tank at the rate of 4 liters/min and the mixture is drained from the tank at the rate of 2 liters/min. Determine the quantity Q(t) of salt in the tank at time t = 0 until the time when the tank overflows. Code a C program which determined this quantity Q(t) by using RK4 method with h = 1. Note: May use the concept of function prototypes, function definition, function call, recursion etc. in a program. 2. A team of surveyors conducted depth-sounding at equidistant locations across the river to measure the area of a river cross-section. Determine the area of the cross-section by coding a C program of the Composite Simpson Rule, taking into consideration the river's 6.0 m width and the fact that it is equally divided into 7 stations. Station Depth, m 0 1 -1.23 24555 3 6 7 -2.08 -2.57 -1.86 -0.65 -0.24 Note: Determine the…7. For each of the following equations of lines in x-y coordinates, find the values of ‘p’ and ‘θ’ in the polar system given as: “p=xcos θ + ysin θ”: a) x=4 b) y=10 c) x=y4- The potential difference 2 points between two point in an electric circuit is 24 V, If 0.4 J of energy were dissipated in a period of 5 ms, what would the current be between the two points? *
- A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 6 m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are 30° and 45° respectively. Find the height of the tower. (Take √3=1.73)Calculate the value of g and h in the following equation.14. The angles of yaw, pitch and roll are determined by the relative positions of the following coordinate systems: Normal earth-fixed axis system and Body axis system ◇ Normal earth-fixed axis system and air-path axis system Body axis system and air-path axis system
- 5. The function y = a + b ·x² is a solution to one of these differential equations for all a and all b. Using dsolve, find the DE. a. y y" (y)² = 0 b. xy'-y (1 + x) = 0 c. xy" - y' = 0 d. xy" + y = 0I 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/:Suppose 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.
- 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 60m2. 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.Suppose 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.