1. Supposed a ball is thrown straight up in the air with an initial velocity of 50 feet per second and an initial height of 5 feet. How high will the ball be after 3 seconds? Note: The height after t seconds is given by the expression - 16t+vot+ho, where ve is the initial velocity and he is the initial height
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1. Supposed a ball is thrown straight up in the air with an initial velocity of 50 feet per second and an initial height of 5 feet. How high will the ball be after 3 seconds? Note: The height after t seconds is given by the expression - 16t+vot+ho, where ve is the initial velocity and he is the initial height.
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- Q10: Using (ode45, ode23, or ode15s), solve the below dynamic electrical system differential equation. 1. The charge Q(t) on the capacitor in the electrical circuit shown satisfies the differential equation where d²Q dQ 1 +R- + √ √e dt2 dt L = 0.5 R = 6.0 C= 0.02 and V(t) is the applied voltage. V(t) = V(t), henrys is the coil's inductance ohms is the resistor's resistance farads is the capacitor's capacitance ellee (i) Is the circuit oscillatory? (ii) If V(t) = 24 sin(10r) volts and Q(0) = 0 = Q'(0), find Q(t). (iii) Sketch the transient solution, the steady state solution, and the full solution Q(t).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 programThe 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,
- Aerospace engineers sometimes compute the trajectories of projectiles such as rockets. A related problem deals with the trajectory of a thrown ball. The trajectory of a thrown by a right fielder is defined by the (x,y) coordinates as displayed in the Figure below. Find the appropriate initial angle θ0 , if v0 = 30m/s, and the distance to the catcher is 90 m. Note that the throw leaves the right fielder’s hand at an elevation of 1.8 m and the catcher receives it at 1 m. Also, you have to write your Matlab code.Interest on a credit card’s unpaid balance is calculated using the average daily balance. Suppose that netBalance is the balance shown in the bill, payment is the payment made, d1 is the number of days in the billing cycle, and d2 is the number of days payment is made before billing cycle. Then, the average daily balance is: averageDailyBalance =netBalance x d1-payment x d2d1 If the interest rate per month is, say, 0.0152, then the interest on the unpaid balance is: Interest= averageDailyBalance * 0.0152 Write a program using c++ compiler that accepts as inputnetBalance, payment, d1,d2, and interest rate per month. The program outputs the interest. Format your output to two decimal places.(Mechanics) The deflection at any point along the centerline of a cantilevered beam, such as the one used for a balcony (see Figure 5.15), when a load is distributed evenly along the beam is given by this formula: d=wx224EI(x2+6l24lx) d is the deflection at location x (ft). xisthedistancefromthesecuredend( ft).wistheweightplacedattheendofthebeam( lbs/ft).listhebeamlength( ft). Eisthemodulesofelasticity( lbs/f t 2 ).Iisthesecondmomentofinertia( f t 4 ). For the beam shown in Figure 5.15, the second moment of inertia is determined as follows: l=bh312 b is the beam’s base. h is the beam’s height. Using these formulas, write, compile, and run a C++ program that determines and displays a table of the deflection for a cantilevered pine beam at half-foot increments along its length, using the following data: w=200lbs/ftl=3ftE=187.2106lb/ft2b=.2fth=.3ft
- Algorithms Question Three points P, Q, and R are said to be collinear if they are on a single line. To check whether the 3 points lie on the same line, we use the distance formula. If P, Q and R are three collinear points, then: Distance from P to Q + Distance from Q to R = Distance from P to R PQ + QR = PR The distance between two points (x1, y1) and (x2, y2) is given by Hence, we can easily find the distance between the points P, Q and R, with the help of this formula. Design an algorithm (pseudocode) to check whether three points are collinear. In your solution include the input and the output.Assignment No. 1 (contd.) You will use Newton-Raphson method to find the eigenvalues. So we rewrite the equations as: fever (E) = VE + Vo sin (a VE+ Vo) V-E cos (a VE + Vo ) = o fodia( E) = VE + Vo cos (a VE+ Vo) + v-E sin (a VE + Vo) = 0 COS To find the eigenvalues of the even states, you must find the zeros of fever (E) and for the odd states you must find the zeros of fodd(E). To use the Newton-Raphson method, you will also need to find the deriva- tives of these functions. Write a MATLAB code to implement the Newton-Raphson Method. Now comes the need for physical insight. Recall three conclusions from your Phy 301 course: (1) For symmetric systems, the lowest eigenstate is always an even state, and (2) The eigenstates alternate between even and odd states, and (3) the bound state eigenvalues lie between 0 and -Vo. So first find the lowest eigenvalue Eo by solving ferer(E) = 0 and your starting guess should be close to -Vo. To find the next eigenvalue Ej solve fodad(E) = 0 and your…A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 10° F. After one-half minute the thermometer reads 57° F. What is the reading of the thermometer at t = 1 min? Assume that the rate of change of temperature in time is proportional to the difference between the thermometer's temperature and the air temperature. Type your answer in °F in the space provided below. Round your answer to two decimal places.
- Draw a Crow's feet ERD using the following information.Using Matlab. Monte Carlo methods are a class of computational methods that rely on repeated random sampling to compute their results. In this problem, you will use the Monte Carlo method to estimate the temperature at an arbitrary point in a uniform solid. Specifically, we will consider the solid object shown below. The temperatures of all surfaces are 500 des F with the exception of the two shaded surfaces, which are at 0 deg F. Inputs to the program should be: 1. The number of random walkers. 2. The (x,,2) coordinates of the point at which the temperature is to be estimated. 3. Plot interval (eg., you may want 1,000,000 random walkers in the simulation but may want to plot after every 10,000). Output from the program should be: 1. A graph of the estimated temperature, plotted according to the plot interval 2. Numerical value of the estimated temperature. USING MATLABIn the example below, the sum of the fourth powers of each digit that forms the 4-digit numbers gives the number itself: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474 = 94 + 44 + 74 + 44 And sum of these numbers is 1634 + 8208 + 9474 = 19316. Find the sum of all numbers that can be written as the sum of the fifth forces of their numbers. (P.s.: You have to done it by C++)