I have to calculate how long a distance an object can manage to fall during 30 seconds of free fall.
All I know is the equation: m*dv/dt=1/2*p*C_D*A*v^2 - mg (where v(t) is velocity at time t, p is the air-density, A is the cross-section area of the object, C_D is a "drag"-coefficient).
I also know the solution to the differential equation as being: v(t)= -v_infinity*tanh(gt/v_infinity).
We can also assume that the initial velocity is 0.
I've been adviced to solve the problem using the following
equation:
Homework Answers
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I have to calculate how long a distance an object can manage to
fall during 30...
If a body of mass m falling from rest under the action of gravity encounters an...
If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of the velocity, then the body's velocity t sec into dv the fall satisfies the differential equation m- mg-kv, where k is a constant that depends on the body's aerodynamic properties and the density of the air. (Assume dt that the fall is short enough so that the variation in the air's density will not affect the outcome...
(1 point) An object of mass 5 kg is given an upward initial velocity of 16...
(1 point) An object of mass 5 kg is given an upward initial velocity of 16 m/sec and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is -50, where v is the velocity of the object in m/sec. Assume gravitational constant is g = 9.8m/seca. Set up the differential equation for this scenario: v' = m/sec Solve the differential equation for the equation of motion: The equation is both...
NOTES: HI, PLEASE SOLVE BY USING ANALYTICAL METHOD WHICH IS RELATED TO FLUID MECHANICS(DRAG FORCE).TQ 25.19...
NOTES: HI, PLEASE SOLVE BY USING ANALYTICAL METHOD WHICH IS
RELATED TO FLUID MECHANICS(DRAG FORCE).TQ
25.19 Assuming that drag is proportional to the square of velocity, we can model the velocity of a falling object like a parachutist with the following differential equation: dv dt where v is velocity (m/s), 1 = time (s), g is the acceleration due to gravity (9.81 m/s), c = a second-order drag coefficient (kg/m). and m 90-kg object with a drag coefficient of 0.225...
2 A robot-arm drive system for one joint can be represented by the differential equation dv...
2 A robot-arm drive system for one joint can be represented by the differential equation dv kvt)k2y(t)+ kyi(t) dt position, and i(t) is the control-motor current velocity, y(t) Where v(t) Derive the state-space equation of the system a) (5 marks) b) By using Routh-Hurwitz criterion, determine the conditions for k,k2,and ky so that the system remains stable? (5 marks)
2 A robot-arm drive system for one joint can be represented by the differential equation dv kvt)k2y(t)+ kyi(t) dt position, and...
1. The cantilever beam AB of length L shown in Fig.(a carries a uniformly distributed load of int...
1. The cantilever beam AB of length L shown in Fig.(a carries a uniformly distributed load of intensity wo, which includes the weight of the beam. Equation of the elastic curve is given by the following differential equation Af _irer where M is the bending moment of the beam. it is also given that of the beam and I modulus of Inertia. where E- Modulus of the elasticity v is the deflection of the beam. Compute the maximum displacement of...
Please do the problem if you can do ALL parts. t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capa...
Please do the problem if you can do ALL parts.
t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capacitor at t 0. b. Write a node equation at node a fort2 0. c. Represent v(t) as a function of i(t) on the series connection of R2 and L. Find dv(t)/dt. Derive a second-order differential...
Lets begin with the assumption that R=kv. What are the units of the coefficient k in...
Lets begin with the assumption that R=kv. What are the units
of the coefficient k in terms of kilograms, metere, and/or
seconds?
dv 6. The equation of motion now becomes mº mg - Kv. dt This equation is also separable because all the terms involving v can be brought to the left side of the dv equation: 1 = 1. dig-(K/m) As before, we integrate both sides of the equation with respect to t and use a change of variables....
In matlab I have created the following function that calculates the distance a projectile travels when...
In matlab I have created the following function that calculates the distance a projectile travels when shot from a cannon given initial velocity and theta. function [distance, xplot, yplot] = Cannon_lab8(V, theta) g = -9.81; % gravity m/s^2 k = 0.35; % drag coefficient Vx = V*cos(theta); %velovity in x-direction Vy = V*sin(theta); %velovity in y-direction dt = 0.01; % seconds, time step x = 0; y = 0; xplot(1) = 0; yplot(1) = 0; i = 2; while y...
In matlab I have created the following function function [distance, xplot, yplot] = Cannon_lab8(V, theta) %...
In matlab I have created the following function function [distance, xplot, yplot] = Cannon_lab8(V, theta) % the function calculates the distance a projectile travels when shot from % a cannon given initial velocity and theta. g = -9.81; % m/s^2 k = 0.35; % drag coefficient Vx = V*cos(theta); Vy = V*sin(theta); dt = 0.01; % seconds x = 0; y = 0; xplot(1) = 0; yplot(1) = 0; i = 2; while y >= 0 ax = -k*Vx; ay...
Here is the task: You are tracking the velocity and position of a rocket-propelled object near...
Here is the task:
You are tracking the velocity and position of a rocket-propelled
object near the surface of Mars. The velocity is v(t) and the
position is s(t), where t is measured in seconds, s in meters, and
v in meters per second. It is known that the v(t) = ds/dt = 4.94 –
3.72t and s(0) = 5.
A. Explain why the condition “f is continuous over [a, b]” from
the Evaluation Theorem is fulfilled by this scenario....
If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of the velocity, then the body's velocity t sec into dv the fall satisfies the differential equation m- mg-kv, where k is a constant that depends on the body's aerodynamic properties and the density of the air. (Assume dt that the fall is short enough so that the variation in the air's density will not affect the outcome...
(1 point) An object of mass 5 kg is given an upward initial velocity of 16 m/sec and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is -50, where v is the velocity of the object in m/sec. Assume gravitational constant is g = 9.8m/seca. Set up the differential equation for this scenario: v' = m/sec Solve the differential equation for the equation of motion: The equation is both...
NOTES: HI, PLEASE SOLVE BY USING ANALYTICAL METHOD WHICH IS
RELATED TO FLUID MECHANICS(DRAG FORCE).TQ
25.19 Assuming that drag is proportional to the square of velocity, we can model the velocity of a falling object like a parachutist with the following differential equation: dv dt where v is velocity (m/s), 1 = time (s), g is the acceleration due to gravity (9.81 m/s), c = a second-order drag coefficient (kg/m). and m 90-kg object with a drag coefficient of 0.225...
2 A robot-arm drive system for one joint can be represented by the differential equation dv kvt)k2y(t)+ kyi(t) dt position, and i(t) is the control-motor current velocity, y(t) Where v(t) Derive the state-space equation of the system a) (5 marks) b) By using Routh-Hurwitz criterion, determine the conditions for k,k2,and ky so that the system remains stable? (5 marks)
2 A robot-arm drive system for one joint can be represented by the differential equation dv kvt)k2y(t)+ kyi(t) dt position, and...
1. The cantilever beam AB of length L shown in Fig.(a carries a uniformly distributed load of intensity wo, which includes the weight of the beam. Equation of the elastic curve is given by the following differential equation Af _irer where M is the bending moment of the beam. it is also given that of the beam and I modulus of Inertia. where E- Modulus of the elasticity v is the deflection of the beam. Compute the maximum displacement of...
Please do the problem if you can do ALL parts.
t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capacitor at t 0. b. Write a node equation at node a fort2 0. c. Represent v(t) as a function of i(t) on the series connection of R2 and L. Find dv(t)/dt. Derive a second-order differential...
Lets begin with the assumption that R=kv. What are the units
of the coefficient k in terms of kilograms, metere, and/or
seconds?
dv 6. The equation of motion now becomes mº mg - Kv. dt This equation is also separable because all the terms involving v can be brought to the left side of the dv equation: 1 = 1. dig-(K/m) As before, we integrate both sides of the equation with respect to t and use a change of variables....
Here is the task:
You are tracking the velocity and position of a rocket-propelled
object near the surface of Mars. The velocity is v(t) and the
position is s(t), where t is measured in seconds, s in meters, and
v in meters per second. It is known that the v(t) = ds/dt = 4.94 –
3.72t and s(0) = 5.
A. Explain why the condition “f is continuous over [a, b]” from
the Evaluation Theorem is fulfilled by this scenario....
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