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I am having trouble with this computer aided engineering problem in Matlab.
- A two-inch diameter craft ball is thrown vertically. The initial velocity of the ball is 20 ft/s.
- Neglecting drag, draw a free body diagram and formulate a first order ODE that governs the velocity of the ball. Is the ODE linear or non-linear?
- Use Euler’s first order method to determine the “drag free” time required to achieve maximum elevation. Check your solution with the analytic solution to the ODE that governs the motion of the ball.
- Drag force is known to be proportional to the velocity squared. Draw a free body diagram and formulate a first order ODE that governs the actual velocity of the ball. Is the ODE linear or non-linear?
To determine the drag coefficient effect, an experiment has been conducted that showed the terminal velocity of the ball (during a free fall) to be 20 ft/s. Use Euler’s method to estimate the “actual” time to achieve maximum elevation for the case that the ball is thrown up with the given initial velocity (20 ft/s).
I worked out the v(t) = -32.2 * t + 20
continuing from here is giving me issue. Any hints or examples would be apprciated.
Transcribed Image Text:2. A two-inch diameter craft ball is thrown vertically. The initial velocity of the ball
is 20 ft/s.
a. Neglecting drag, draw a free body diagram and formulate a first order
ODE that governs the velocity of the ball. Is the ODE linear or non-
linear?
b. Use Euler's first order method to determine the “drag free” time required
to achieve maximum elevation. Check your solution with the analytic
solution to the ODE that governs the motion of the ball.
c. Drag force is known to be proportional to the velocity squared. Draw a
free body diagram and formulate a first order ODE that governs the actual
velocity of the ball. Is the ODE linear or non-linear?
d. To determine the drag coefficient effect, an experiment has been
conducted that showed the terminal velocity of the ball (during a free fall)
to be 20 ft/s. Use Euler's method to estimate the "actual" time to achieve
maximum elevation for the case that the ball is thrown up with the given
initial velocity (20 ft/s).
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Step 1: Draw a free body diagram and formulate a first order ODE that governs the velocity of the ball
VIEW Step 2: Use Euler’s first order method to determine the drag free time required to achieve maximum elevation
VIEW Step 3: Drag force is known to be proportional to the velocity squared. Draw a free body diagram and formula
VIEW Step 4: Determine the drag coefficient effect.
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