1. Set-up the appropriate differential equation(s) and solve to derive the general equation of motion for...

Set-up the appropriate differential equation(s) and solve to derive the general equation of motion for a human sized “dummy” moving vertically (up/down) under the following assumptions:

(a)The initial elevation is h0 ft.

(b)The initial velocity is V0 ft./sec.

(c)All motion vertical (ignore any sideways motion).

(d)The force due to wind is proportional to velocity and in the opposite

direction of velocity.

(e)The “terminal velocity” is 120mph (e.g. lim t→∞ (V)= 120 mph).

(f)Force = Mass * Acceleration.

(g)Acceleration due to gravity = 32 ft/sec^2

Assume the dummy is ejected from a test balloon and has initial elevation of 10 miles and initial velocity of 100mph (straight up)

(a) Determine and simplify the equation of motion for this situation

(b) Determine the maximum height, hmax, of the dummy

(c)Determine the dummy’s height at time t = 60 sec

(d)Determine when the dummy will hit the ground in seconds

(e)Determine the speed of the dummy at impact

Repeat (2) using Newton’s equations and compare the answers to those obtained from your model

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

solve the differential equation a) ? ′′ − ? ′ = 1 1 + ? −?...

solve the differential equation a) ? ′′ − ? ′ = 1 1 + ? −? b) ? ′′ + 3? ′ + 2? = cos(?x ) c) 10) ? ′′ − 2? ′ + ? = exsqrtx

Solve the given differential equation using an appropriate substitution. The DE is a Bernoulli equation, A....

Solve the given differential equation using an appropriate substitution. The DE is a Bernoulli equation, A. dy/dx = y(xy^6 - 1) B. x dy/dx + y = 1/y^2 C. t^2 dy/dt + y^2 = ty

5. Solve the following differential equation using the given initial conditions (Use convolution and set up the...

5. Solve the following differential equation using the given initial conditions (Use convolution and set up the integral but do not integrate.) y'’ − 2y’ + 2y = 18e−t sin3t; y(0) = 0, y’(0) = 3

write a differential equation in terms of displacement s to model the motion of an undamped...

write a differential equation in terms of displacement s to model the motion of an undamped vertical spring with mass m. recall that the weight should equal the spring's restoring force

Show the differential equation is not exact and by finding an appropriate integrating factor solve the...

Show the differential equation is not exact and by finding an appropriate integrating factor solve the given initial problem. (yx+y^2+ y) dx + (x+2y) dy =0

Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. dy dx...

Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. dy dx = y − x y + x

Set up the appropriate form of the particular solution to each of the differential equations below,...

Set up the appropriate form of the particular solution to each of the differential equations below, but do NOT determine the values of the coefficients. (a) y′′ +10y′ +25y=2e^(5t) +te^(−5t) b) y′′ +9y=5t^2 +4cos(3t)+6e^(3t)

convert differential equation to a matrix differential equation? can put an example and solve it.

1) Use MATLAB to solve this differential equation. ??/?? = .25? (1 − ?/4 ) -...

1) Use MATLAB to solve this differential equation. ??/?? = .25? (1 − ?/4 ) - a 2) Use MATLAB to graph solution curves to this system with several different initial values. Be sure to show at least one solution curve for each of the scenarios found in ??/?? = .25? (1 − ?/4 ) - a ( let a = 0.16)

Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where...

Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where x=[x(t)y(t)]. x(t)= y(t)= please be as clear as possible especially when solving for c1 and c2 that's the part i need help the most

Subjects