Question

In: Advanced Math

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

1.

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

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

3.

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

Expert Solution

Colby Messinger answered 2 years ago

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